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  • ...proximating <math>N(N+1) \approx N^2</math>, we were looking for a perfect square that is close to, but less than, <math>4032</math>. Since <math>63^2 = 3969 Knowing that each row number can stand for the number of coins there are in the row, we can just add until we get <math>2016</mat
    2 KB (395 words) - 22:29, 3 December 2024
  • ...are arguably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four sig For two [[number]]s <math>a</math> and <math>b</math>:
    12 KB (1,806 words) - 05:07, 19 June 2024
  • ...inequality''' is an [[inequality]] that states that the square of any real number is nonnegative. Its name comes from its simplicity and straightforwardness. For all [[real number]]s <math>x</math>, <math>x^2 \ge 0</math>.
    3 KB (583 words) - 20:20, 2 August 2024
  • ...s the highest power of the variable which appears in the polynomial. This number is known as the ''degree'' of the polynomial and is written <math>\deg(P)</ ...Fundamental Theorem of Algebra]] states that any polynomial with [[complex number|complex]] coefficients can be written as
    6 KB (1,100 words) - 14:57, 30 August 2024
  • ...olve more than algebra problems, sometimes going into other topics such as number theory. *Two different [[prime number]]s between <math>4</math> and <math>18</math> are chosen. When their sum is
    4 KB (682 words) - 12:13, 8 December 2024
  • ===Proof that the square root of 2 is irrational=== Assume <math>\sqrt{2}</math> is [[rational number|rational]], i.e. it can be expressed as a rational fraction of the form <ma
    2 KB (374 words) - 13:01, 21 August 2022
  • ...must be incorrect; at least one box must contain two or more balls. <math>\square</math> ...ber of red, blue, yellow, and black socks in a drawer, what is the minimum number of socks that the Martian must pull out of the drawer to guarantee they hav
    11 KB (1,986 words) - 18:13, 19 June 2024
  • ...th>x</math> such that <math>P = x^4 + 6x^3 + 11x^2 + 3x + 31</math> is the square of an integer. Then <math>n</math> is: ...say <math>P=(x^2+3x+1)^2-3(x-10)=a^2</math>, where <math>a^2</math> is the square of an integer mentioned on the problem. Right from here, we can set <math>x
    3 KB (571 words) - 23:42, 21 October 2021
  • '''Number theory''' is the field of [[mathematics]] associated with studying the prop Number theory is a broad topic, and may cover many diverse subtopics, such as:
    3 KB (404 words) - 19:56, 28 December 2024
  • '''Fermat's Little Theorem''' is highly useful in [[number theory]] for simplifying the computation of exponents in [[modular arithmet If <math>{a}</math> is an [[integer]], <math>{p}</math> is a [[prime number]] and <math>{a}</math> is not [[divisibility|divisible]] by <math>{p}</math
    16 KB (2,660 words) - 22:42, 28 August 2024
  • ...]]. If <math>n</math> is a positive integer, <math>\phi{(n)}</math> is the number of integers in the range <math>\{1,2,3\cdots{,n}\}</math> which are relativ ...}</math> is allowed since it is relatively prime to <math>m</math>. <math>\square</math>
    4 KB (569 words) - 21:34, 30 December 2024
  • ...ed equal to <math>\frac{n(n+1)}{2}</math> (the <math>n</math>th triangular number is defined as <math>1+2+\cdots +n</math>; imagine an [[equilateral polygon ...n can be useful in almost any branch of mathematics. Often, problems in [[number theory]] and [[combinatorics]] are especially susceptible to induction solu
    5 KB (768 words) - 23:59, 28 September 2024
  • ...ve at our answer: <math>9 \cdot 10 \cdot 10 \cdot 10 = 9000</math>. <math>\square</math> ...ht lead one to think. All we did was think about constructing a four-digit number by choosing its digits, compute the possible numbers each digit can be, and
    13 KB (2,018 words) - 14:31, 10 January 2025
  • ...n four letters long and contain only the letters A, B, C, D, and E. <math>\square</math> ...<math>68+53=121</math> positive integer solutions to the equation. <math>\square</math>
    5 KB (709 words) - 16:40, 24 September 2024
  • A '''prime number''' (or simply '''prime''') is a [[positive integer]] <math>p>1</math> whose ...osite number|composite]] because it is its only factor among the [[natural number|natural numbers]].
    6 KB (1,053 words) - 20:29, 7 January 2025
  • ...ative. The range is the set of all non-negative real numbers, because the square root can never return a negative value.
    10 KB (1,761 words) - 02:16, 12 May 2023
  • ...where one counts what they don't want, then subtracts that from the total number of possibilities. In problems that involve complex or tedious [[casework]], ...>19</math> of them. Thus, our answer is is <math>99-19 = 80</math>. <math>\square</math>
    8 KB (1,192 words) - 16:20, 16 June 2023
  • ...o choose <math>k-1</math> things from <math>n-1</math> things added to the number of ways to choose <math>k</math> things from <math>n-1</math> things. &=&\binom{n}{k}. \qquad\qquad\square\end{eqnarray*}</cmath>
    12 KB (1,993 words) - 22:47, 27 October 2024
  • ...tosthenes''' is a simple method to quickly uncover a short list of [[prime number]]s. ...aximal number you are interested in. Now, during each step, take the first number that is neither crossed out nor circled, circle it, and cross all larger nu
    1 KB (212 words) - 20:16, 7 December 2007
  • ...n=kd</math> or, in other words, if <math>\frac nd</math> is also a natural number (i.e <math>d</math> divides <math>n</math>). See [[Divisibility]] for more A common notation to indicate a number is a divisor of another is <math>n|k</math>. This means that <math>n</math>
    1 KB (274 words) - 18:50, 29 August 2023

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