Question

show that every positive integer can be expressed as 5q or 5q+1or5q+2or 5q+3or5q+4or 5q+5.plz answer this in a systematic wayyyyy..........!!!!?!!!☝️☝️☝️✍️✍️✍️✍️✍️

Answer 1

Heya!!

Sol :
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 this helps you ☺☺