Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Functions

Olympiad workbook · IOQM · Functions

Find the largest value of a^b such that the positive integers a,...

Find the largest value of

a^b

such that the positive integers

a, b>1

satisfy

a^b b^a+a^b+b^a=5329

.

Correct answer

81

Step-by-step solution

\begin{aligned} & \left(a^b+1\right)\left(b^a+1\right)=5330=2 \times 5 \times 13 \times 41 \\ & \Rightarrow \quad a^b=81=3^4 \text { and } b^a=64=4^3 \end{aligned}

Or

a^b=64=4^3

and

b^a=81=3^4

\therefore a^b=81

Practice Functions on Quantrex Academy →

More from Functions

Let n be a positive integer such that 1 ≤ n ≤ 1000 . Let M_n be the number of integers in… Olympiad workbook Positive integers x, y, z satisfy x y+z=160 . Compute the smallest possible value of x+y… Olympiad workbook Consider the sequence of number [n+ 2 n +(1)/(2)] for n ≥ 1 , where [x] denotes the… Olympiad workbook Let x_1 be a positive real number and for every integer n ≥ 1 let x_ n+1 =1+x_1 x_2 … …… Olympiad workbook Let f: ℝ arrow ℝ be a function satisfying the relation 4 f(3-x)+3 f(x)=x^2 for any real x… Olympiad workbook Let f(x)= (x)/(3)+ (3 x)/(10) for all real x . Find the least natural number n such that… Olympiad workbook The sum of [x] for all real numbers x satisfying the equation 16+15 x+15 x^2=[x]^3 is: Olympiad workbook Let P(x)=a_0+a_1 x+a_2 x^2+… .+a_n x^n be a polynomial in which a_i is non-negative… Olympiad workbook Full Functions list All Olympiad workbook PYQs