By using PMI prove that , 4^n+15^n leaves remainder 1 when divided by 9 . Share with your friends Share 0 Lovina Kansal answered this Dear student Let P(n) be the statement given byP(n): 4n+15n when divided by 9,the remainder is 1.or, P(n): 4n+15n=9k+1 for some k∈NSTEP 1: P(1)=41+151=4+15=19=9k+1 where k=2∴P(1) is true.STEP 2: Let P(m) be true.Then, 4n+15n=9k+1 for some k∈N.We shall now show that P(m+1) is true for which we have to show that 4m+1+15m+1when divided by 9 ,the remainder is 1 i.e., 4m+1+15m+1=9λ+1 for some λ∈NNow, 4m+1+15m+1=4m.4+15m.15Please recheck your question because we cannot proceed further now to prove the desired result. Regards -1 View Full Answer
