Question

show that the square of any positive integer in the form of 10p,10p+2 or 10p+4​

Answer 1

Answer:

Let a be any positive integer and b = 4.

Then, by Euclid's algorithm a = 4q + r for some integer q  0 and 0  r < 4

Thus, r = 0, 1, 2, 3

Since, a is an odd integer, so a = 4q + 1 or 4q + 3

Case I: When a = 4q + 1

Squaring both sides, we have, a2 = (4q + 1)2

a2 = 16q2 + 1 + 8q

   = 8(2q2 + q) + 1

    = 8m + 1, where m = 2q2 + q

Case II: When a = 4q + 3

Squaring both sides, we have,

a2 = (4q +3)2

   = 16q2 + 9 + 24q

   = 16 q2 + 24q + 8 + 1

    = 8(2q2 + 3q + 1) +1

    = 8m +1 where m = 2q2 + 3q + 1

Hence, a is of the form 8m + 1 for some integer m.

Step-by-step explanation:

do it the same way using ur common sense

and if u dont hv it

its not my problem

Answer 2

Answer:

pls replace 3 by 10 as I have no much time being a topper of class 10