# 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

Could you show that it was true for 24,25,26,27,28 then just say that every number beyond these can be expressed as x + 5n, where x is one of 24,25,26,27,28 and n is a natural number?

3. Sep 30, 2009

### ipitydatfu

lol yeah. i kinda figured it out similar to that way after taking a long nap. thanks for the response though!