Find the number of solutions
Probability
Level
5
Find the number of integral solutions of the equation .
The answer is 50000.
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1 solution
prime factorization of any of xi's=(2^a1)X(3^b1)X(5^c1)X(7^d1)X(11^e1)
a1+a2+...+a5=1 has 5 solutions.Same for b,c,d,e. Now total no. of +ve sol.=5^5=3125.But other types are (+,+,-,-,-)&(-,-,-,-,+).So total no. of types are (5C2+5C4+1)=16.
REQD. NO. OF SOLN.=-16X3125=50000.