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show that square of any positive integer of the form 5m+1 will leave the remainder 1 when divided by 5 for some integer n
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show that square of any positive integer of the form 5m+1 will leave t...
(5m+1)2 = 25m2+1+10m
Here the term 25m2 is divisible by 5 and the term 10m is also exactly divisible by 5.
Therefore it leaves the remainder 1.
Putting m = 1, we get; (5X1+1)2 = 62 = 36
And 36 when divided by 5, leaves the remainder 1.
Therefore square of any positive integer is of the form 5m+1 will leave the remainder 1 when divided by 5 for some integer m.

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show that square of any positive integer of the form 5m+1 will leave the remainder 1 when divided by 5 for some integer n Related: Euclid Division Lemma - Real Numbers, Class 10 Mathematics
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