Show that any positive odd integer is of the form 5q+1,or 5q+2 ,or 5q+

1.	Show that any positive odd integer is of the form 5q+1,or 5q+2 ,or 5q+3, 5q+4
Answer» Thanks you Let x be any positive integerThen x = 5q or x = 5q+1 or x = 5q+4 for integer x.If x = 5q, x2\xa0= (5q)2\xa0= 25q2\xa0= 5(5q2) = 5n (where n = 5q2\xa0)If x = 5q+1, x2\xa0= (5q+1)2\xa0= 25q2+10q+1 = 5(5q2+2q)+1 = 5n+1 (where n = 5q2+2q )If x = 5q+4, x2\xa0= (5q+4)2\xa0= 25q2+40q+16 = 5(5q2\xa0+ 8q + 3)+ 1 = 5n+1 (where n = 5q2+8q+3 )∴in each of three cases x2\xa0is either of the form 5q or 5q+1\xa0or 5q+4 and for integer q.

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