04m and n are two odd partive setegeretProve that m?taz Meven bet notd

1.	04m and n are two odd partive setegeretProve that m?taz Meven bet notdiuirtlete bi
Answer» Since m and n are odd positive integers, so let m = 2q + 1 and n = 2p + 1 , •°• m² + n² = ( 2q + 1 )² + ( 2p + 1 )² . = 4( q² + p² ) + 4( q + p ) + 2 . = 4{( q² + p² + q + p )} + 2 . = 4y + 2 , where y = q² + p² + q + p is an integer . •°• q² + p² is even and leaves remainder 2, when divided by 4 that is not divisible by 4.

04m and n are two odd partive setegeretProve that m?taz Meven bet notdiuirtlete bi

Answer»

Since m and n are odd positive integers, so let m = 2q + 1 and n = 2p + 1 ,

•°• m² + n² = ( 2q + 1 )² + ( 2p + 1 )² .

= 4( q² + p² ) + 4( q + p ) + 2 .

= 4{( q² + p² + q + p )} + 2 .

= 4y + 2 , where y = q² + p² + q + p is an integer .

•°• q² + p² is even and leaves remainder 2, when divided by 4 that is not divisible by 4.