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2. Integer-valued function - Wikipedia

   en.wikipedia.org/wiki/Integer-valued_function

   In mathematics, an integer-valued function is a function whose values are integers.In other words, it is a function that assigns an integer to each member of its domain.. The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful.

3. Exponentiation - Wikipedia

   en.wikipedia.org/wiki/Exponentiation

   When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243 . The base 3 appears 5 times in the multiplication, because the exponent is 5 .

4. Bernoulli's inequality - Wikipedia

   en.wikipedia.org/wiki/Bernoulli's_inequality

   Bernoulli's inequality can be proved for case 2, in which is a non-negative integer and , using mathematical induction in the following form: we prove the inequality for r ∈ { 0 , 1 } {\displaystyle r\in \{0,1\}} ,

5. Exponentiation by squaring - Wikipedia

   en.wikipedia.org/wiki/Exponentiation_by_squaring

   The method is based on the observation that, for any integer >, one has: = {() /, /,. If the exponent n is zero then the answer is 1. If the exponent is negative then we can reuse the previous formula by rewriting the value using a positive exponent.

6. List of integer sequences - Wikipedia

   en.wikipedia.org/wiki/List_of_integer_sequences

   A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...

7. Proof of Fermat's Last Theorem for specific exponents

   en.wikipedia.org/wiki/Proof_of_Fermat's_Last...

   In the centuries following the initial statement of the result and before its general proof, various proofs were devised for particular values of the exponent n. Several of these proofs are described below, including Fermat's proof in the case n = 4, which is an early example of the method of infinite descent.

8. List of Mersenne primes and perfect numbers - Wikipedia

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

   The following is a list of all 52 currently known (as of January 2025) Mersenne primes and corresponding perfect numbers, along with their exponents p. The largest 18 of these have been discovered by the distributed computing project Great Internet Mersenne Prime Search , or GIMPS; their discoverers are listed as "GIMPS / name ", where the name ...

9. Legendre's formula - Wikipedia

   en.wikipedia.org/wiki/Legendre's_formula

   As one special case, it can be used to prove that if n is a positive integer then 4 divides () if and only if n is not a power of 2. It follows from Legendre's formula that the p -adic exponential function has radius of convergence p − 1 / ( p − 1 ) {\displaystyle p^{-1/(p-1)}} .