A number theory problem by rajdeep brahma
Number Theory
Level
4
Find the number of ordered triplets of integers such that .
240
60
120
40
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1 solution
72=3^2X2^3. x=3^(a1)X2^(b1)... Write prime factorisation of y & z similarly. a1+a2+a3=2 #solutions=6. b1+b2+b3=3 #solutions=10. total #sol. for +ve integers=60. (x,y,z) a tuple implies (x,-y,-z),(-x,y,-z),(-x,-y,z) to be a tuple.
NO. OF SOLUTIONS=60X4=240