Question

induction

Answer 1

\[\forall n \in \mathbb{Z}^+,n>14 \exists i,j \in \mathbb{N} [n=3i+8j]\]

Answer 2

Perhaps you could prove it only for all numbers in the least common multiple of 3, 8. That way, perhaps then you can just extend it to all n. Maybe that would be a use of the strong form of induction.

Answer 3

base case \[P(14)\]
\[14=3(2)+8(1)\]
\[i=2,j=1\]
TRUE

Answer 4

\[P(k)\]
\[k=3i+8j\]
\[P(k+1)\]
\[k+1=3i+8j\]

Answer 5

your k = k+1. You've done something wrong.

Answer 6

where \[i>2,j>1\]