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The subject matter of this work are the two equations:x^4+y^4+z^4-2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)= n (1) Andx^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^4)(z^4)= n (2) where n is a natural number.  Contest Corner problem CC24, published in the May2012 issue of the journalCrux Mathematicorum(see reference[1]); provided the motivation behind thiswork. In Th.1, we show that eq.(1) if n=8N, N odd; then eq.(1) has no integersolutions; which generalizes problem CC24(the case n=24).  We use Th.2, to find some rational solutions of eq.(1); which answers thesecond question in CC24. In Th.4, we show that if n= p, 4, or pq; where p and qare distinct primes. Then eq.(1)has no integer solutions. In Th.6, we determineall the integer solutions to (1), when n=p^2, p an odd prime. Theorems 7through13, deal with equation (2). In Th.11, we determine all the integersolutions of eq.(2). Th.12 states that (2) has no integer solutions in n iscongruent to 2 or 3 modulo4. Finally, in Th.13 we determine all the rationalsolutions of eq.(2).

Integer Solutions, Rational solutions of the equations x^4+y^4+z^4  -2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)=n and  x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^2)(z^2)=n; And Crux Mathematicorum Contest  problem CC24