Question

prove that x and y are odd positive integer and x² + y² is an even integer but not divisible by 4 .​

Answer 1

Since x and y are odd positive integers so

Let x = 2n + 1 and y = 2m + 1

x² + y² = (2n + 1)² + (2m + 1)²

= 4(n² + m²) + 4(n + m) + 2

= 4 {(n² + m² + n + m}) + 2

= 4q + 2

Where q = n² + m² + n + m is an integer

Since

x² + y² is even and leaves remainder 2 when divided by 4

Not divisible by 4

Answer 2

ꜱᴇᴇ ᴛʜᴇ ɢɪᴠᴇɴ ᴀᴛᴛᴄʜᴍᴇɴᴛ ꜰᴏʀ ᴍᴏʀᴇ ᴅᴇᴛᴀɪʟ

ℏṽḙ ᾰ ℵჄḉ ∂ᾰჄ ᾰℏḙᾰ∂