MathDB

4

Part of 2011 NZMOC Camp Selection Problems

Problems(2)

(m + 1)! + (n + 1)! = m^2n

Source: New Zealand NZMOC Camp Selection Problems 2011 Juniors 4

9/18/2021
Find all pairs of positive integers mm and nn such that (m+1)!+(n+1)!=m2n.(m + 1)! + (n + 1)! = m^2n.
diophantineDiophantine equationnumber theory
ABxAD=BPxDP+APxCP if <APB+<CP D=180^o, # (2011 NZOMC Camp Sel. S4)

Source:

1/4/2021
Let a point PP inside a parallelogram ABCDABCD be given such that ∠APB+∠CPD=180o\angle APB +\angle CPD = 180^o. Prove that AB⋅AD=BP⋅DP+AP⋅CPAB \cdot AD = BP \cdot DP + AP \cdot CP.
geometryparallelogram