N≡1(bmod2k) for all k=1 to n ⇒N−1 is divisible by LCM of all 2k for k=1 to n LCM(2,4,8,...,2n)=2n Calculations: N−1= multiple of 2n N=2n×k+1 We want the smallest N≥10000 Try values of n : n=13⇒213=8192 ⇒N=8192×2+1=16385 n=14⇒214=16384 ⇒N=16384×1+1=16385 n=14 follows the condition.
