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Find the number of positive integral ordered pairs a, b satisfying the equation a^b + b^a = 100

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Find the number of positive integral ordered pairs a, b satisfying the equation a^b + b^a = 100
posted Jun 16, 2018 by anonymous
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Find the number of ordered pairs (x,y) satisfying the system of equations - a) x+y^2 = 12 b) x^2 + y = 12

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a^2 + b^2 = ab, a = b = 0 satisfies the equation. But is there another pair of real numbers satisfying this equation?

a^2 + b^2 = a.b
It is obvious that a=b=0 satisfies the equation above. But is there another pair of real numbers satisfying this equation?

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