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?


[number theory](/questions/number-theory_90)
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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.

