Math Forum :: View topic – Mathematical Induction

Let P(n) be the proposition that ” 5^2n-1 – 3^2n-1 – 2^2n-1 is divisible by 15″ for some positive integers of n. When n=1, 5-3-2=0 which is divisible by 15. So, P(1) is true. Assume P(k) is true, i.e. 5^2k-1 – 3^2k-1 – 2^2k-1 =15M , where M is an integer. When n=k+1, =5^2k – 3^2k – 2^2k =15M(5M+k) As, 15M(5M+k)is an integer. Therefore, 15M(5M+k) is divisible by 15. Therefore, P(k+1) is also true. By the principle of mathemical induction, P(n) is true for some positive integers n._________________

1+1= 2 or 1+1=11 (rejected)