prove that 152n-1+ 1 is divisible by 16 - Maths - Principle of Mathematical Induction

Question

prove that 152n-1+ 1 is divisible by 16

Rishabh Mittal · Accepted Answer

Let pn: 152n-1+1 is divisible by 16For n=1p1:152-1+1=15+1=16, which is divisible by 16So , pn is true for n=1Let us assume that pn is true for n=kpk: 152k-1+1 is divisible by 16152k-1+1=16dFor n=k+1pk+1:152k+1-1+1=152k+2-1+1=152 
 152k-1 +1=152152k-1+1-1+1=225152k-1+1-225+1=22516d-224=16225d-14=16p                                       Say p=225d-14So , it is true for n=k+1 Hence by PMI , it is true for all n∈N

prove that 152n-1+ 1 is divisible by 16 .

prove that 15^2n-1+ 1 is divisible by 16 .