Prove that square of integer is in the form of 5m+1 is in the same for

1.	Prove that square of integer is in the form of 5m+1 is in the same form
Answer» l Step-by-step explanation: Let a be any positive integer, such that a= bq+r b= 5 ,so r=1,2,3,4,0. if.r=0 a=5Q+r a=5q+0 SQUARE on both sides a²=( 5q)16 a²=25q² a²=5(5q)² a²=5M if r=1 a=5q+1 square on both sides a²=(5q+1)16 a²= (5q)²+ (1)²+2(5q)(1) a²= 25q+1+10q a²=5(5q+2) +1 a²= 5m +1

Prove that square of integer is in the form of 5m+1 is in the same form

Answer»

Step-by-step explanation:

Let a be any positive integer, such that a= bq+r

b= 5 ,so r=1,2,3,4,0.

if.r=0

a=5Q+r

a=5q+0

SQUARE on both sides

a²=( 5q)16

a²=25q²

a²=5(5q)²

a²=5M

if r=1

a=5q+1

square on both sides

a²=(5q+1)16

a²= (5q)²+ (1)²+2(5q)(1)

a²= 25q+1+10q

a²=5(5q+2) +1

a²= 5m +1

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