Question

Why every odd square can be written in the form of 4k+1?

Answer 1

by euclid division lemma a=bq+r

Answer 2

by Euclid lemma any number is of the form 2k or 2k+1

${(2k + 1)}^{2} = 4 {k}^{2} + 4k + 1 \\ = 4( {k}^{2} + k) + 1 \\ = 4m + 1$