Question

Prove that the square of any positive integer of the form 5q + 1 is of the same form.

Answer 1

SOLUTION :  

Since positive integer n is of the form 5q + 1

Let n = 5q + 1, then

n² = (5q + 1)²

[On squaring both sides]

n² = (5q)² + 2(1) (5q) + 1²

[(a+b)² = a² + b² + 2ab]

n²  = 25q² + 10q + 1

n² = 5(5q² + 2q)+1

n² = 5m + 1, where m = 5q² + 2q

Hence n²  is of the form 5m + 1.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

hello mate

here is your prooving

for any postive integer is in the form of 5q+1

sqauring the no.  (5q +1)^2   = 25 q2 + 10 q +1            

-----------> 5 (5 q2 + 2q ) +1

-----------> 5 m +1    .( where m is the value of any positive integer = 5q2 + 2q )

hope this would help you