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Always zero or four (Posted on 2018-12-16)

Consider the integer powers of 7: a(n) = 7^n:
7, 49, 343, 2401, 16807,... 117649, ...

Prove that the second from right digit in all those numbers (excluding the 1st) is either 0 or 4.

No Solution Yet Submitted by Ady TZIDON

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Solution (spoiler)

Comment 1 of 1

Mod 100. the powers of 7 cycle through

07 etc.

therefore, the tens digit of any power is 4 or 0

Posted by Steve Herman on 2018-12-16 09:16:04

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