Although I saw two different posts with this error message nothing worked with me:
Error:(25, 17) Failed to resolve: org.mockito:mockito-core:1.10.19
I tried to change the Mockito dependency using compile, androidTestCompile and testCompile and in the global Gradle file I tried to add Maven as repository but did not work.
EDIT: I am using Android Studio 2.1
This is my app build.gradle
apply plugin: 'com.android.application'
android {
compileSdkVersion 24
buildToolsVersion "24.0.0"
defaultConfig {
    applicationId "ivano.android.com.mockitoexample"
    minSdkVersion 15
    targetSdkVersion 24
    versionCode 1
    versionName "1.0"
}
buildTypes {
    release {
        minifyEnabled false
        proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
    }
}
}
dependencies {
compile fileTree(dir: 'libs', include: ['*.jar'])
compile 'com.android.support:appcompat-v7:24.2.1'
testCompile 'junit:junit:4.12'
testCompile 'org.mockito:mockito-core:1.10.19'
}
and this the global one
// Top-level build file where you can add configuration options common to all sub-projects/modules.
buildscript {
    repositories {
        jcenter()
    }
    dependencies {
        classpath 'com.android.tools.build:gradle:2.1.0'
        // NOTE: Do not place your application dependencies here; they belong
        // in the individual module build.gradle files
    }
}
allprojects {
    repositories {
        jcenter()
    }
}
task clean(type: Delete) {
    delete rootProject.buildDir
}