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1

Part of 2001 Irish Math Olympiad

Problems(2)

equation

Source: Ireland 2001

7/5/2009
Find all positive integer solutions (a,b,c,n) (a,b,c,n) of the equation: 2^n\equal{}a!\plus{}b!\plus{}c!.
modular arithmeticnumber theory unsolvednumber theory
find a number

Source: Ireland 2001

7/5/2009
Find the least positive integer a a such that 2001 2001 divides 55^n\plus{}a \cdot 32^n for some odd n n.
modular arithmeticnumber theory unsolvednumber theory