problem on functions?

Question

P(a,b) = P(a-b,b) if a>= b and
P(a,b) = a if a < b


it is given that P(a,7) = 4; P(a,11) = 6 and P(a,13) = 3.
Find P(a,17), if ‘a’ is a positive integer between 2000 and 3000.

(1) 6(2) 8 (3) 11 (4) 12

Answer 1

Assuming a and b are positive integers, your definition of P(a,b) is equivalent to:

P(a,b) = a (mod b)

So a is the solution to:

a = 4 (mod 7)
a = 6 (mod 11)
a = 3 (mod 13)

This has a unique solution mod (7*11*13=1001):

a = 809 (mod 1001)

Since 2000 < a < 3000:

a = 2811

-->

a = 6 (mod 17)

-->

Answer is 6 (choice 1)