Question

PLEASE HELP!!!
Prove that square of any positive integer id of the form 5q, 5q+1, 5q+4 for some integer q.....
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Answer 1

Step-by-step explanation:

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Answer 2

Let x be any positive integer

then , x = 5q or x = 5q + 1 orx= 5q + 4

for integer x

If x = 5q

x² = (5q)² = 25q² = 5(5q)² = 5n

where n = 5q²

If x = 5q + 1

x² = (5q + 1)² = 25q² + 10q + 1

= 5(5q² + 2q) + 1 = 5n + 1

where n = 5q² + 2q

If x = 5q + 4

x² = (5q + 4)² = 25q² + 40q + 16

= 5(5q² + 8q + 3) + 1 = 5n + 1

where n = 5q² + 8q + 3

∴ In each three cases x² is either of the form 5q or 5q+1 or 5q+4 and for integer q.