That's a Big Power

Number Theory Level 3

For how many integers $a$ , with $1\le a\le 16$ , is $a^{2015}+a^{ 2016}$ divisible by 5?

12 8 4 5 3 7 6

1 solution

Sabhrant Sachan
May 3, 2016

$\text {We have, } a^{2015}+a^{2016} \\ \implies a^{2015}(a+1) \text { should be divisible by 5} \\ a=5n-1\color{#D61F06}{\text { OR }}5n \text { Where n belong to An integer } \\ \text {So , Possible value of n } = 1,2,3 \implies a=4,5,9,10,14,15 \\ \color{#3D99F6}{\boxed{\text{Ans = } 6 }}$

That's a Big Power

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