Hi the problem is in FileDownloader class

 urlConnection.setRequestMethod("GET");
    urlConnection.setDoOutput(true);

You need to remove the above two lines and everything will work fine. Please mark the question as answered if it is working as expected.

Latest solution for the same problem is updated Android PDF Write / Read using Android 9 (API level 28)

Attaching the working code with screenshots.

MainActivity.java

package com.example.downloadread;

import java.io.File;
import java.io.IOException;

import android.app.Activity;
import android.content.ActivityNotFoundException;
import android.content.Intent;
import android.net.Uri;
import android.os.AsyncTask;
import android.os.Bundle;
import android.os.Environment;
import android.view.Menu;
import android.view.View;
import android.widget.Toast;

public class MainActivity extends Activity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
    }

    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        // Inflate the menu; this adds items to the action bar if it is present.
        getMenuInflater().inflate(R.menu.main, menu);
        return true;
    }

    public void download(View v)
    {
        new DownloadFile().execute("http://maven.apache.org/maven-1.x/maven.pdf", "maven.pdf"); 
    }

    public void view(View v)
    {
        File pdfFile = new File(Environment.getExternalStorageDirectory() + "/testthreepdf/" + "maven.pdf");  // -> filename = maven.pdf
        Uri path = Uri.fromFile(pdfFile);
        Intent pdfIntent = new Intent(Intent.ACTION_VIEW);
        pdfIntent.setDataAndType(path, "application/pdf");
        pdfIntent.setFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);

        try{
            startActivity(pdfIntent);
        }catch(ActivityNotFoundException e){
            Toast.makeText(MainActivity.this, "No Application available to view PDF", Toast.LENGTH_SHORT).show();
        }
    }

    private class DownloadFile extends AsyncTask<String, Void, Void>{

        @Override
        protected Void doInBackground(String... strings) {
            String fileUrl = strings[0];   // -> http://maven.apache.org/maven-1.x/maven.pdf
            String fileName = strings[1];  // -> maven.pdf
            String extStorageDirectory = Environment.getExternalStorageDirectory().toString();
            File folder = new File(extStorageDirectory, "testthreepdf");
            folder.mkdir();

            File pdfFile = new File(folder, fileName);

            try{
                pdfFile.createNewFile();
            }catch (IOException e){
                e.printStackTrace();
            }
            FileDownloader.downloadFile(fileUrl, pdfFile);
            return null;
        }
    }


}

FileDownloader.java

package com.example.downloadread;

import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.net.HttpURLConnection;
import java.net.MalformedURLException;
import java.net.URL;

public class FileDownloader {
    private static final int  MEGABYTE = 1024 * 1024;

    public static void downloadFile(String fileUrl, File directory){
        try {

            URL url = new URL(fileUrl);
            HttpURLConnection urlConnection = (HttpURLConnection)url.openConnection();
            //urlConnection.setRequestMethod("GET");
            //urlConnection.setDoOutput(true);
            urlConnection.connect();

            InputStream inputStream = urlConnection.getInputStream();
            FileOutputStream fileOutputStream = new FileOutputStream(directory);
            int totalSize = urlConnection.getContentLength();

            byte[] buffer = new byte[MEGABYTE];
            int bufferLength = 0;
            while((bufferLength = inputStream.read(buffer))>0 ){
                fileOutputStream.write(buffer, 0, bufferLength);
            }
            fileOutputStream.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        } catch (MalformedURLException e) {
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}

AndroidManifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.example.downloadread"
    android:versionCode="1"
    android:versionName="1.0" >

    <uses-sdk
        android:minSdkVersion="14"
        android:targetSdkVersion="18" />
    <uses-permission android:name="android.permission.INTERNET"></uses-permission>
    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE"></uses-permission>
    <uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"></uses-permission>
    <uses-permission android:name="android.permission.READ_PHONE_STATE"></uses-permission>
    <application
        android:allowBackup="true"
        android:icon="@drawable/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >
        <activity
            android:name="com.example.downloadread.MainActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>

</manifest>

activity_main.xml

<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:paddingBottom="@dimen/activity_vertical_margin"
    android:paddingLeft="@dimen/activity_horizontal_margin"
    android:paddingRight="@dimen/activity_horizontal_margin"
    android:paddingTop="@dimen/activity_vertical_margin"
    tools:context=".MainActivity" >

    <Button
        android:id="@+id/button1"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_alignParentLeft="true"
        android:layout_alignParentTop="true"
        android:layout_marginTop="15dp"
        android:text="download"
        android:onClick="download" />

    <Button
        android:id="@+id/button2"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_alignParentLeft="true"
        android:layout_alignParentRight="true"
        android:layout_below="@+id/button1"
        android:layout_marginTop="38dp"
        android:text="view"
        android:onClick="view" />

</RelativeLayout>

The possible reason is the folder in which you want to does not exist. First check if it exist. Create it if not. Then create fileoutputstream and write to it.

As an alternative you can try opening pdf in google docs. Try below code-

   String pdfurl = "http://www.example.com/yourfile.pdf";
   String googleDocsUrl = "http://docs.google.com/viewer?url="+pdfurl;
   Intent intent = new Intent(Intent.ACTION_VIEW);
   intent.setDataAndType(Uri.parse(googleDocsUrl ), "text/html");
   startActivity(intent);

Thanks to @blackapps I solved the issue:

try {
    url = new URL(bookURL);
} catch (MalformedURLException e) {
    e.printStackTrace();
}

DownloadManager.Request request = new DownloadManager.Request(Uri.parse(url + ""));
request.setTitle(fileName);
request.setMimeType("application/pdf");
request.allowScanningByMediaScanner();
request.setAllowedOverMetered(true);
request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);
request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, "AldoFiles/" + fileName);
DownloadManager downloadManager = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
downloadManager.enqueue(request);

When you call DownloadFile(File d, String f, String n), how do you get the directory?

If you are using the getExternalStorageDirectory (i'm assuming you are), that pdf is private to your application, and can't be accessed by other applications.

If you need to keep that file private to your application, and still be able to open using another application, use a ContentProvider

If you can keep that file on a shared directory, you should use getExternalStoragePublicDirectory() to get the path to save the file, and later on to retrieve the file URI.

This problem is related to this one, hence the similar answer.

This should solve the problem:

Inside showPDF:

String extStorageDirectory = Environment.getExternalStoragePublicDirectory(
        Environment.DIRECTORY_DOWNLOADS).toString();

Inside displayPdf

File file = new File(Environment.getExternalStoragePublicDirectory(Environment.DIRECTORY_DOWNLOADS) + "/pdf/" + pdf_name + ".pdf");