prove that the square of any positive integer is of the form of 5q ,5q + 1 ,5q + 4 for some integer q
Answers
Answered by
6
Answer:
Let x be any positive integer .
Then x = 5q or x = 5q+1 or x = 5q+4 for integer x.
If x = 5q, x2 = (5q)2 = 25q2 = 5(5q2) = 5n (where n = 5q2 )
If x = 5q+1, x2 = (5q+1)2 = 25q2+10q+1 = 5(5q2+2q)+1 = 5n+1 (where n = 5q2+2q )
If x = 5q+4, x2 = (5q+4)2 = 25q2+40q+16 = 5(5q2+ 8q + 3)+ 1 = 5n+1 (where n = 5q2+8q+3 )
∴in each of three cases x2 is either of the form 5q or 5q+1 or 5q+4 and for integer q.
HOPE IT HELPS !!!
Let x be any positive integer .
Then x = 5q or x = 5q+1 or x = 5q+4 for integer x.
If x = 5q, x2 = (5q)2 = 25q2 = 5(5q2) = 5n (where n = 5q2 )
If x = 5q+1, x2 = (5q+1)2 = 25q2+10q+1 = 5(5q2+2q)+1 = 5n+1 (where n = 5q2+2q )
If x = 5q+4, x2 = (5q+4)2 = 25q2+40q+16 = 5(5q2+ 8q + 3)+ 1 = 5n+1 (where n = 5q2+8q+3 )
∴in each of three cases x2 is either of the form 5q or 5q+1 or 5q+4 and for integer q.
HOPE IT HELPS !!!
Kashashok:
actually this is wrong
why is it so
if u could do it correctly then paste it here
Answered by
10
Answer:
please dude mark my answer as brainlist
Attachments:
Similar questions