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>

Like this:

Intent browserIntent = new Intent(Intent.ACTION_VIEW, Uri.parse("*url for your pdf*"));
startActivity(browserIntent);

This will cause the pdf to be downloaded in the notification bar, as if you had initiated the download through the browser.

Check this question if you have problems: How can I open a URL in Android's web browser from my application?

You can view or download the pdf by either of the two ways i.e by opening it in device in-built browser or in the webview by embedding it in your app.

To open the pdf in browser,

Intent browserIntent = new Intent(Intent.ACTION_VIEW, Uri.parse(pdf_url));
startActivity(browserIntent);

Instead to open in webview,

 WebView webView = (WebView) findViewById(R.id.webView1);
 webView.getSettings().setJavaScriptEnabled(true);
 webView.loadUrl(pdf_url);