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• Mathematical notation
  For <math>n \in \mathbb{Z}^*</math> to be '''[[squarefree]]''' means that there is no integer <math>k>1</math> with <math>k^2|n</math ...on''': <math>\mu(n): = \begin{cases} 0 & \textrm{ if } n\; \textrm{ is not squarefree} \ (-1)^s & \textrm{ where } s \;\textrm{ is the number of prime factors o
  8 KB (1,410 words) - 09:32, 24 February 2025
• 2022 USAJMO Problems/Problem 1
  <math>m</math> satisfies the conditions precisely when <math>m</math> is not squarefree. ...o construct a solution for all other values of <math>m</math> that are not squarefree.
  4 KB (653 words) - 04:52, 10 March 2025
• Mock AIME 2 2006-2007 Problems/Problem 7
  ...the length of this path is <math>m\sqrt{n},</math> where <math>n</math> is squarefree, find <math>m+n.</math>
  1 KB (231 words) - 18:10, 10 July 2014
• Mock AIME 6 Pre 2005/Problems
  ...>\displaystyle a\pi+b\sqrt{c}</math> where <math>\displaystyle c</math> is squarefree, find <math>\displaystyle a+b+c</math>.
  7 KB (1,110 words) - 05:15, 31 December 2006
• 2010 USAJMO Problems/Problem 1
  ...p(f(a_k))</math>. Also, since <math>f(k)</math> and <math>f(a_k)</math> is squarefree, <math>v_p(k), v_p(a_k) \leq 1</math>. Thus, <math>v_p(k \cdot a_k) = 1</ma
  12 KB (2,336 words) - 15:28, 28 October 2024
• Mock AIME I 2012 Problems
  ...rm <math>a\sqrt{b}+c\sqrt{d}+e</math> where <math>b, d</math> are distinct squarefree integers. Find <math>a+b+c+d+e</math>.
  7 KB (1,309 words) - 11:13, 8 April 2012
• Mock AIME I 2012 Problems/Problem 7
  ...rm <math>a\sqrt{b}+c\sqrt{d}+e</math> where <math>b, d</math> are distinct squarefree integers. Find <math>a+b+c+d+e</math>.
  2 KB (400 words) - 09:58, 11 March 2025
• Algebraic number theory
  ...some fixed, [[squarefree]] <math>n</math> (if <math>n=x^2y</math> is not [[squarefree]], the case is equivalent to <math>n=y</math>). More specifically, the ques
  10 KB (1,646 words) - 15:04, 28 May 2020
• 2013 Mock AIME I Problems
  ...can be expressed in the form <math>a+b\sqrt{c}</math>, for <math>b</math> squarefree. Compute <math>a+b+c</math>.
  7 KB (1,159 words) - 09:15, 30 July 2024
• 2025 AIME II Problems/Problem 12
  ...}{q}</math> for positive integers <math>m,n,p,q</math> with <math>n</math> squarefree and <math>\gcd(m,p,q)=1</math>, find <math>m+n+p+q</math>.
  2 KB (352 words) - 23:03, 15 February 2025
• 2021 GCIME Problems
  ...of <math>\triangle DEF</math> can be written as <math>a\sqrt{b}</math> for squarefree <math>b</math>. What is <math>a+b</math>?
  4 KB (651 words) - 20:18, 6 March 2021
• G285 2021 Summer Problem Set
  ...th>m\sqrt{n}+o\sqrt{p}</math>, where <math>n</math> and <math>p</math> are squarefree,. Find <math>m+n+o+p</math>
  9 KB (1,577 words) - 23:28, 28 June 2021
• 2022 SSMO Accuracy Round Problems
  ...math>c</math> are relatively prime positive integers and <math>b</math> is squarefree, find <math>a+b+c.</math>
  5 KB (830 words) - 13:04, 14 December 2023
• 2022 SSMO Team Round Problems
  ...> can be expressed as <math>\frac{\sqrt{m}}{n},</math> with <math>m</math> squarefree. Find <math>m+n</math>. ...ath> can be expressed as <math>m\sqrt{n}</math>, where <math>n</math> is a squarefree positive integer. Find <math>m+n</math>.
  9 KB (1,537 words) - 11:13, 25 December 2023
• 2022 SSMO Relay Round 2 Problems
  ...uch that <math>a</math> and <math>d</math> are positive, <math>c</math> is squarefree, and <math>\gcd{(a, b, d)}=1</math>, find the value of <math>a+b+c+d.</math
  2 KB (291 words) - 21:56, 31 May 2023
• 2022 SSMO Accuracy Round Problems/Problem 3
  ...math>c</math> are relatively prime positive integers and <math>b</math> is squarefree, find <math>a+b+c.</math>
  501 bytes (89 words) - 13:02, 14 December 2023
• 2022 SSMO Team Round Problems/Problem 7
  ...> can be expressed as <math>\frac{\sqrt{m}}{n},</math> with <math>m</math> squarefree. Find <math>m+n</math>.
  373 bytes (66 words) - 13:06, 14 December 2023
• 2022 SSMO Team Round Problems/Problem 12
  ...ath> can be expressed as <math>m\sqrt{n}</math>, where <math>n</math> is a squarefree positive integer. Find <math>m+n</math>.
  743 bytes (124 words) - 13:07, 14 December 2023
• 2022 SSMO Relay Round 2 Problems/Problem 1
  ...uch that <math>a</math> and <math>d</math> are positive, <math>c</math> is squarefree, and <math>\gcd{(a, b, d)}=1</math>, find the value of <math>a+b+c+d.</math
  648 bytes (125 words) - 13:10, 14 December 2023
• 2023 SSMO Accuracy Round Problems
  ...of the diagonals of <math>ABCD</math> is <math>a\sqrt{b},</math> for some squarefree <math>b,</math> find <math>a+b.</math>
  6 KB (891 words) - 03:41, 23 December 2023

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