Express any number greater than 35 as sum of x 5s and y 9s

Apr 2019
4
0
india
How can we prove that any number greater than or equal to 35 as a sum of x 5s and y 9s
Probably by induction
 
Jun 2019
445
237
USA
y = 0: 35, 40, 45, 50, 55, 60, …
y = 1: 39, 44, 49, 54, 59, …
y = 2: 38, 43, 48, 53, 58, …
y = 3: 37, 42, 47, 52, 57, …
y = 4: 36, 41, 46, 51, 56, …

That's all integers >= 35.
You could also probably build a more formal proof using \(\displaystyle mod 5\), but the above should be sufficient.
 
Feb 2010
715
150
31 is the largest non expressible number. Any number greater than or equal to 32 can be expressed. The proof uses something called strong induction.