Question

Show that square of any positive integer cannot be of the form 7q+3or 7q+5 or 7q+6 for any integer q

Answer 1

Answer:

let a=bq+r

Step-by-step explanation:

where b=7. r=0,1,2,3,4,5,6,

when r=0. a=7q

when r=3 a=7q+3.

when r=5 a=7q+5

when r=6. a=7q+6

Answer 2

Answer:

Numbers divisible by 7 can be of the form :

d = 7m + r

where, 0 ≤ r < 7

If d = 7m, d² = 7q

where q is some integer and q = 7m²

If d = 7m + 1, d² = 7q + 1

If d = 7m + 2, d² = 7q + 4

If d = 7m + 3, d² = 7q + 4

If d = 7m + 4, d² = 7q + 1

If d = 7m + 5, d² = 7q + 4

If d = 7m + 6, d² = 7q + 4

If d = 7m + 7, d² = 7q + 1

Therefore , the square of any positive integer cannot be in the form of 7q + 3 or 7q + 5 or 7q + 6 for any integer 'q'