Assume $n$ is a Natural Number which satisfies the following 2 properties simultaneously:
$01$ . $(3n+1)$=$a$12 for some Natural Number $a$1.
$02$ . $(4n+1)$=$a$22 for some Natural Number $a$2.
Prove that $n$ is divisible by $56$.
For example, if we take $n$=$56$, we have $(3n+1)$=$169$=$13$2 and $(4n+1)$=$225$=$15$2.
I could prove that $n$ is a multiple of $4$ but coud not proceed any further.However my strategy was to prove that $n$ is divisible by 8 & then that $n$ is divisible by 7 because $G.C.D (7,8)=1$ and $L.C.M.(7,8)=56$.