Prove by mathematical induction: 3^4n+2 + 5^2n+1 is a multiple of 14 Share with your friends Share 3 Aarushi Mishra answered this Pn: 34n+2+52n+1 is a multiple of 14Pn: 34n+2+52n+1=14k, k∈ℕP1: 36+53=729+125=854=1461hence P1 is trueLet Pm be truePm:34m+2+52m+1=14k', k'∈ℕPm+1:34m+1+2+52m+1+1=14k'', k''∈ℕL.H.S.34m+1+2+52m+1+1=34m+4+2+52m+1+1=3.4 34m+2+52m+1+1Using Pm34m+2=14k'-52m+1=3.4 14k'-52m+1+52m+1+2=81 14k'-52m+1+52. 52m+1=1481k'-81.52m+1+25. 52m+1=1481k'-56.52m+1=1481k'-4.52m+1=14k'', where k''=81k'-4.52m+1Hence Pm+1 is true, therefore, Pn is true 14 View Full Answer
