2016 AMC 8 Problem 24 Number Theory

2016 AMC 8 Problem 24 Number Theory

 Understand the Problem The digits , , , , and  are each used once to write a five-digit number . The three-digit number  is divisible by , the three-digit number  is divisible by , and the three-digit number  is divisible by . What is ? Source of the problem 2016 AMC...
2017 AMC 8 Problem 21 Number Theory

2017 AMC 8 Problem 21 Number Theory

Understand the problem Suppose , , and  are nonzero real numbers, and . What are the possible value(s) for           ? Source of the problem 2017 AMC 8 Problem 21 Topic Number Theory Difficulty Level Easy Suggested Book Excursion in Mathematics Start with hints Hint...
SMO(senior)-2014 Problem 2 Number Theory

SMO(senior)-2014 Problem 2 Number Theory

Understand the problem Find, with justification, all positive real numbers      satisfying the system of equations:     Source of the problem SMO (senior)-2014 stage 2 problem 2 Topic Number Theory Difficulty Level Easy Suggested Book Excursion in Mathematics Start...
SMO (senior) -2014/problem-4 Number Theory

SMO (senior) -2014/problem-4 Number Theory

Understand the problem For each positive integer  let    where     are the first  primes. Prove that for each positive integer , there is an integer  such that    Source of the problem SMO (senior)-2014 stage 2 problem 4 Topic Number Theory Difficulty Level Medium...
2018 AMC 10A Problem 25 Number Theory

2018 AMC 10A Problem 25 Number Theory

Understand the problem For a positive integer  and nonzero digits , , and , let  be the -digit integer each of whose digits is equal to ; let  be the -digit integer each of whose digits is equal to , and let  be the -digit (not -digit) integer each of whose digits is...