Problem 3079. Big numbers, repeated least significant digits

Created by Michael C.

Difficulty:Rate

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This problem builds off of Problem 3077
Given an integer x which contains d digits, find the value of (minimum) n (n > 1) such that the last d digits of x^n is equal to x. If the last d digits will never equal x, return inf.
Example 1:
x = 2; (therefore d = 1)
2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32
n = 5;
Example 2:
x = 10; (therefore d = 2)
10^2 = 100, 10^3 = 1000, etc
n = inf;

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330 Solutions
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Last Solution submitted on Mar 02, 2025

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3 Comments

3 Comments

rifat on 14 Mar 2015

is it correct for 35197? Im getting 5001 instead of inf.

Tim on 15 Mar 2015

I also get 5001.

Rafael S.T. Vieira on 3 Sep 2020

10016 and 10081 have another valid answer: 1251 (besides 626). The problem should accept them or request the minimum exponent.

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Project Euler II

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