MATHS
posted by JESS .
prove by mathematical induction that 7^n+4^n+1 is divisible by 6

MATHS 
Reiny
7^n + 4^n + 1
1. test for n = 1
7^1 + 4^1 + 1 = 12 , which is divisible by 6
2. assume it is true for n = k , that is, assume that
7^k + 4^k + 1 is divisible by 6
3. then show that 7^(k+1) + 4^(k+1)  1 is divisible by 6
use the number property that if both A and B are divisble by c
then AB is divisible by c
e.g. 156 and 117 are both divisible by 13
then is 156117 or 39 divisible by 13 ? YES
so ...
7^(k+1) + 4^(k+1) + 1  (7^k + 4^k + 1)
= 7^(k+1) + 4^(k+1) + 1 7^k  4^k  1
= 7^k(71) + 4^k(41)
= 6(7^k) + 3(4^k)
clearl 6(7^k) is a multiple of 6 , thus divisible by 6
and in 3(4^k) , the 4^k must be even and any even times 3 is divisible by 6
so we have shown that the result is divisible by 6
(the sum of multiples of 6 must be divisible by 6)
Respond to this Question
Similar Questions

Math
Use mathematical induction to prove that 5^(n)  1 is divisible by four for all natural numbers n. Hint: if a number is divisible by 4, then it has a factor of 4. also, 1 = 5 +4 This is a take home test so I don't want the answer … 
Calculus
Use mathematical induction to prove that each proposition is valid for all positive integral values of n. 5^n + 3 is divisible by 4. 
Discrete Math
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³  5(1) = 6, which is divisible … 
Discrete Math
Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1)  2^5(1) = 7, which is divisible by 7. For the inductive case, assume k ≥ … 
Calculus
Prove via Mathematical Induction that (7*n)  1 is divisible by 6. I have that it is divisble when n=1, but not n=2 and so on. How should I write the inductive proofs? 
Math
Use mathematical induction to prove that 2^(3n)  3^n is divisible by 5 for all positive integers. ThankS! 
maths
prove by mathematical induction that 7n+4n+1 is divisible by 6 
Algebra
Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible by 5 
Algebra ASAP
so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers … 
Mathematical Induction
Use mathematical induction to prove that the following is true. 8+11+14...+(3n+5)=1/2n(3n+13), for all n in the set of natural numbers.