Nth Triangular Number
Implement a function that returns the nth triangular number efficiently.
Integer Square Root Floor
Implement a function that returns the greatest integer whose square is ≤ n, using only integer operations.
Euler Totient Function
Implement Euler's totient function φ(n) for positive integers.
Sieve of Eratosthenes
Implement the Sieve of Eratosthenes to return a sorted list of all primes up to a given integer n.
Prime Factorization
Return a sorted list of prime factors of a positive integer, including repeated factors.
Count divisors
Compute the number of positive divisors of a given integer using its prime factorization.
Sum of divisors
Given an integer n, return the sum of all its positive divisors.
Abundant Number Check
Implement a function to check whether a given integer is abundant: sum of proper divisors exceeds the number.
Armstrong Number Check
Implement a function that checks if a given integer is an Armstrong number.
Pentagonal Number
Given a positive integer n, return the nth pentagonal number using the formula P(n) = n(3n - 1)/2.
Partition function
Write a function that returns the number of ways to write a positive integer as a sum of positive integers (order irrelevant).
Multiply without multiply
Write a function that multiplies two integers using only addition, subtraction, and bit shifts — no * operator.
Showing 12 challenges · Math & Number Theory
Math & Number Theory — Python coding challenges
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This page lists math & number theory challenges — real Python problems you solve in the browser IDE with instant test feedback. Each challenge includes a clear brief, starter code, and automated checks.
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