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The square of a positive integer leaves a remainder of 1 when divided by 5. What are the possible remainders when the integer itself is divided by 5?

 Aug 12, 2020
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n    n^2  Remainder when n is divided by 5
1    1       1
4    16    4
6    36    1
9     81   4
11   121   1
14   196  4
16   256  1
19   361  4
21   441  1
24   576  4

There are an infinite number of integers whose squares mod 5 =1 and which leave a remainder of 1 or 4 as you can see on the right hand side.

 Aug 12, 2020

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