Prime divisor

Number Theory Level 2

Find the largest prime divisor of 2015 ! + 2016 ! 2015!+2016!


The answer is 2017.

Áron Bán-Szabó by Áron Bán-Szabó , 17, Hungary

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2 solutions

Rajen Kapur
Aug 14, 2017

Taking 2015! common, the given value is 2015! x (1 + 2016). As 2017 is a prime number, the answer is 2017.

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2015 ! + 2016 ! = 2015 ! + ( 2015 ! ) ( 2016 ) = 2015 ! ( 1 + 2016 ) = 2015 ! ( 2017 ) \color{plum}\large 2015!+2016!=2015!+(2015!)(2016)=2015!(1+2016)=2015!(2017)

since 2017 is a prime number, the answer is 2017. \color{#3D99F6}\large \mbox {since 2017 is a prime number, the answer is 2017.}

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