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  2. Square number - Wikipedia

    en.wikipedia.org/wiki/Square_number

    if the last digit of a number is 4 or 6, its square ends in an odd digit followed by a 6; and; if the last digit of a number is 5, its square ends in 25. In base 12, a square number can end only with square digits (like in base 12, a prime number can end only with prime digits or 1), that is, 0, 1, 4 or 9, as follows:

  3. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    In other words, the square of a number is the square of its difference from 100 added to the product of one hundred and the difference of one hundred and the product of two and the difference of one hundred and the number. For example, to square 93: 100(100 − 2(7)) + 7 2 = 100 × 86 + 49 = 8,600 + 49 = 8,649

  4. List of numbers - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/List_of_numbers

    A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.

  5. List of Mersenne primes and perfect numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_Mersenne_primes...

    [3] Perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4]

  6. Powerful number - Wikipedia

    en.wikipedia.org/wiki/Powerful_number

    A powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full.

  7. Euclid number - Wikipedia

    en.wikipedia.org/wiki/Euclid_number

    Every Euclid number is congruent to 3 modulo 4 since the primorial of which it is composed is twice the product of only odd primes and thus congruent to 2 modulo 4. This property implies that no Euclid number can be a square. For all n ≥ 3 the last digit of E n is 1, since E n − 1 is divisible by 2 and 5.

  8. 1089 (number) - Wikipedia

    en.wikipedia.org/wiki/1089_(number)

    1089 is widely used in magic tricks because it can be "produced" from any two three-digit numbers. This allows it to be used as the basis for a Magician's Choice. For instance, one variation of the book test starts by having the spectator choose any two suitable numbers and then apply some basic maths to produce a single four-digit number. That ...

  9. Sum of two squares theorem - Wikipedia

    en.wikipedia.org/wiki/Sum_of_two_squares_theorem

    The number of representable numbers in the range from 0 to any number is proportional to ⁡, with a limiting constant of proportionality given by the Landau–Ramanujan constant, approximately 0.764. [3] The product of any two representable numbers is another representable number.