# Help with induction?

1. Sep 29, 2009

### ipitydatfu

Question Details:
show that any number greater than 23 can be written as a sum of 5's and/or 7's

attempt:
24: 7 7 5 5
25: 5 5 5 5 5
26: 7 7 7 5
27: 7 5 5 5 5
28: 7 7 7 7
29: 7 7 5 5 5
30: 5 5 5 5 5 5
31: 7 7 7 5 5
32: 7 5 5 5 5 5
33: 7 7 7 7 5
34: 7 7 5 5 5 5

from this, i see that this follows a pattern:
n = f(a,b) = 5a + 7b

for n> 23

but how do i go about to prove this for all values?

2. Sep 29, 2009