Question

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

Answer 1

Answer:

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

If true then enter 1 and if false then enter 0

Answer 2

Question ::-.

prove that the square of any positive integer of the form 5q+1 is of the same form ?

Solution ::-.

Let x be a any positive integer of form 5q + 1

=> By Euclid Division Lemma

Value of b = 5

Value of r can be 0,1,2,3,4,

x = bq + r

${x}^{2}$ = ${(5q+1)}^{2}$

${x}^{2}$ = 25${q}^{2}$ + 10q + 1

${x}^{2}$ = 5 ( 5${q}^{2}+ 2q$ ) + 1

${x}^{2}$ = 5 ( 5${q}^{2}+ 2q$ ) + 1

Where , m = ( 5${q}^{2}+ 2q)$

Hence , ${x}^{2}$ = 5m + 1