math myth – 1

  • All square numbers have odd number of factors. All other numbers have even number of factors.
  • To check whether a number is prime, it is sufficient to check its divisibiliy by all prime numbers less than square root of the number.
  • A number n is a sum of two squares if and only if all prime factors of n of the form 4m+3 have even exponent in the prime factorization of n.
  • if p is a prime number, then for any integer a, ap ? a will be evenly divisible by p. This can be expressed in the notation of modular arithmetic as follows.
    ap ? a (mod p) .  This is Fermat’s Little Theorem.
  • If an integer n is greater than 2, then the equation an + bn = cn has no solutions in non-zero integers a, b, and c. This is Fermat’s Last Theorem.
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