MathDB

3

Part of 2017 Hanoi Open Mathematics Competitions

Problems(2)

n^2 + 4n + 25 is perfect square (HOMC 2017 J Q3)

Source:

8/7/2019
Suppose n2+4n+25n^2 + 4n + 25 is a perfect square. How many such non-negative integers nn's are there?
(A): 11 (B): 22 (C): 44 (D): 66 (E): None of the above.
Perfect Squaresnumber theory
diophantine x^4 + 4y^4 + z^4 + 4 = 8xyz (HOMC 2017 S Q3)

Source:

9/8/2019
The number of real triples (x,y,z)(x , y , z ) that satisfy the equation x4+4y4+z4+4=8xyzx^4 + 4y^4 + z^4 + 4 = 8xyz is
(A): 00, (B): 11, (C): 22, (D): 88, (E): None of the above.
Diophantine equationdiophantinenumber theory