Question

use of Euclid division Lemma to show that the square of any positive integer cannot be of the form 5 M + 2 or 5 M + 3 for some integer m

Answer 1

Let a be any positive integer
b=5
By Euclids division lemma
a=5m+r
where q is greater than 0 and r=1,2,3 or 4.
a=5m or a=5m+1 or a=5m+2 or a=5m+3 or a=5m+4
According to theorem If the square of any positive integer is divided then than no. Is only divided by 2.
So, the square is not equal to 5m+2 or 5m+3 .
Hence proved.

Answer 2

Answer:et a be any positive integer

b=5

By Euclids division lemma

a=5m+r

where q is greater than 0 and r=1,2,3 or 4.

a=5m or a=5m+1 or a=5m+2 or a=5m+3 or a=5m+4

According to theorem If the square of any positive integer is divided then than no. Is only divided by 2.

So, the square is not equal to 5m+2 or 5m+3 .

Step-by-step explanation: