MathDB

The triplet of positive integers

(a,b,c)

with

a<b<c

is called a fatal triplet if there exist three nonzero integers

p,q,r

which satisfy the equation

a^p b^q c^r = 1

. As an example,

(2,3,12)

is a fatal triplet since

2^2 \cdot 3^1 \cdot (12)^{-1} = 1

. The positive integer

N

is called fatal if there exists a fatal triplet

(a,b,c)

satisfying

N=a+b+c

. (a) Prove that 16 is not fatal. (b) Prove that all integers bigger than 16 which are not an integer multiple of 6 are fatal.

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