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Find f(1990,31) - ILL 1990 SPA1

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September 19, 2010
functioninductionalgebra unsolvedalgebra

Problem Statement

Function f(x,y):N×N→Qf(x, y): \mathbb N \times \mathbb N \to \mathbb Q satisfies the conditions:
(i) f(1,1)=1f(1, 1) =1,
(ii) f(p+1,q)+f(p,q+1)=f(p,q)f(p + 1, q) + f(p, q + 1) = f(p, q) for all p,q∈Np, q \in \mathbb N, and
(iii) qf(p+1,q)=pf(p,q+1)qf(p + 1, q) = pf(p, q + 1) for all p,q∈Np, q \in \mathbb N.
Find f(1990,31).f(1990, 31).
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