Swapping 3's and 7's

Number Theory Level 2

There is a positive integer N N such that the last digit of N 3 N^3 is 7.

Is there a positive integer M M such that the last digit of M 7 M^7 is 3?

Yes No

Pi Han Goh by Pi Han Goh , 30, Malaysia

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3 solutions

Matin Naseri
Jan 26, 2018

N 3 \text{N}^{3} = 3 3 \text{3}^{3} = 27 \text{27} .

M 7 \text{M}^{7} = 7 7 \text{7}^{7} = 823543 \text{823543} .

Hence the answer is 7.

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7 7 = 823543 7^{7} = 823543

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Sanath Kamath
Jan 26, 2018

7 7 7^7 =823543

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