# It's hard but easy

**Number Theory**Level 5

\[\large \sum { { ({ s }_{ i }+{ s }_{ k }) }^{ 3 } } \]

\(N\) is natural number such that \({ 2 }^{ n }|N\) for some whole number \(n\).Let \({ s }_{ a }\) be defined as a number formed from last \(a+1\) digits on \(N\).Then find value of above expression modulo \({ 2 }^{ n }\) if \(n-1\le i,k<j\) and \(n+2<j\).

**Details:**

\(1)\) If \(N=123456\) then number \({ s }_{ 3 }\) is \(3456\).

\(2)\) \(j\) is number of digits of \(N\).