SOLUTION: THE NUMBER OF TRIPLES (a,b,c) OF POSITIVE INTEGERS SATISFYING 2^a-(5^b*7^c)=0 IS A. INFINITE, B.2, C.1, D.0

Algebra ->  Finance -> SOLUTION: THE NUMBER OF TRIPLES (a,b,c) OF POSITIVE INTEGERS SATISFYING 2^a-(5^b*7^c)=0 IS A. INFINITE, B.2, C.1, D.0       Log On


   

Question 872659: THE NUMBER OF TRIPLES (a,b,c) OF POSITIVE INTEGERS SATISFYING 2^a-(5^b*7^c)=0 IS
A. INFINITE, B.2, C.1, D.0

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Ea-%285%5Eb%2A7%5Ec%29=0<--->2%5Ea=%285%5Eb%2A7%5Ec%29
2 , 5 , and 7 are prime numbers.
2%5Ea is a multiple of 2 but not a multiple of any other prime number.
2%5Ea=%285%5Eb%2A7%5Ec%29 is not a multiple of 2.
The two expressions can never be the same.
The number of triples satisfying that equation is %220%22 .