Question

Prove that the square of any positive integer is either of the form 5m or 5m+1 or 5m+4 for some integer q​

Answer 1

Step-by-step explanation:

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.