Prove that the square of any positive integer is either of the form 5q or 5q + 1 or 5q+4 for some positive integer q
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SOLUTION:
Let a be the positive even integer then a is form of 5p
2
a = (5p) square
= 25p square
= 5(5p square) {where 5p square = q}
=5q
--------------- if a is an odd number then a is in form of 5p+1
2
a = (5p+1 )square
= 25p square +1
=5(5p square )+1 [where 5p square = q]
= 5q +1
--------------if a is a od number in the form 5p+2
2
a = (5p+2) square
= 25p square +4
= 5(5p square)+4 [where 5p square =q]
= 5q +4
hence proved
plzz mark my answer as brainliest and click on heart icon------------------------------
SOLUTION:
Let a be the positive even integer then a is form of 5p
2
a = (5p) square
= 25p square
= 5(5p square) {where 5p square = q}
=5q
--------------- if a is an odd number then a is in form of 5p+1
2
a = (5p+1 )square
= 25p square +1
=5(5p square )+1 [where 5p square = q]
= 5q +1
--------------if a is a od number in the form 5p+2
2
a = (5p+2) square
= 25p square +4
= 5(5p square)+4 [where 5p square =q]
= 5q +4
hence proved
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