Can you think of positive integers a, b such that `a^(b) = b^(a) ` ?

a and b are two positive integers such that a^(b)timesb^(a)=800 . Find the a and b.

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 80 , b = 8

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 13 , b = 3

The number of positive integral ordered pairs of (a ,b) such that 6,a ,b are in harmonic progression is _________.

If a and b are positive numbers such that a^(2) + b^(2) = 4 , then find the maximum value of a^(2) b .

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 132, b = 11

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 125 , b = 5

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.

Statement 1: Let A ,B be two square matrices of the same order such that A B=B A ,A^m=O ,n dB^n=O for some positive integers m ,n , then there exists a positive integer r such that (A+B)^r=Odot Statement 2: If A B=B At h e n(A+B)^r can be expanded as binomial expansion.

Let a , b , c , d be positive integers such that (log)_a b=3/2a n d(log)_c d=5/4dot If (a-c)=9, then find the value of (b-d)dot