Euler's Form for an Odd Perfect Number
\[n\]
is an odd perfect number then it must be off the form \[n=p^kp_1^{2k_1}p_2^{2k_2}...p_r^{2k_r}\]
where each \[p_1, \; i=1, \; 2,..., \; r\]
is a distinct prime greater than 2 and \[p \equiv 1 \; (mod \; 4)\]
.The above result implies that
\[n \equiv 1 \; (mod \; 4)\]
because for any \[p \equiv 3 \; (mod \; 4)\]
, \[p^2=)4c+3)(4c+3)=16c^2+24c+9 \equiv 1 \; (mod \; 4)\]
and any two numbers equiv to 1 (mod 4), when multiplied together, give a number equal to 1 (mod 4)). 
