Question

Prove that the square of any positive integer is of form 5m, 5m+1, 5m + 4 for some integer m.

Answer 1

Answer:

Consider that m=2.square of 2=4, (2×2=4).

5m=5 (2)=10

4 not equals to 10

5m+1=5 (2)+1=11

4 not equals to 11

5m+4=5 (2)+4=14

14 is also not equals to 4.

If we take 5 as "m" then the square of 5=25,which satisfies the condition 5m

hence proved.

only 5 is the number which can satisfies the condition 5m. There is no other number which can satisfies the conditions 5m,5m+1,5m+4.

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