In purity, factoring a number n is simply decomposing it as the product of two smaller non-trivial, i.e. different from 1 and n itself, divisors. But by repeatedly factoring the divisors one will eventually come up with a unique set of primes which, when multiplied together, render the ...
I saw a question somewhere, which asked to find the number of distinct numbers which can be represented as sum of two distinct primes. T=10000,N=10000000, the question felt impossible, so after attempting for a while, I saw the editorial, the solution was incorrect and poorly written. If ...
Do all numbers have an even amount of factors? What is the smallest whole number that has exactly 2 distinct positive divisors? Can three consecutive whole numbers be prime? Assuming that p, q, and r are distinct primes, how many positive divisors does m have? 1) If m = q^3 2) If ...
Find the sum of the numbers less than 200 which have 9 divisors? Assuming that p, q, and r are distinct primes, how many positive divisors does m have? 1) If m = q^3 2) If m= p^(2)q^(2) 3) If m = pqr What is the smallest prime number greater than ...
int *primes,*numbers; int count = 0; primes = malloc(sizeof(int)*PRIMES); numbers = malloc(sizeof(int)*LIMIT); /*fill the array with natural numbers*/ for (i=0;i<LIMIT;i++){ numbers[i]=i+2; } /*sieve the non-primes*/ ...
For example, using the primes 2 3 and 5 again, one could limit the exponent of 2 to fall in the range 0..15, and the exponents of 3 and 5 to fall in the range 0..3; this allows the exponents to be stored in 4, 2, and 2 bits respectively for a total of 8 bits. Such a...
The final value and the initial value of a particular variable can be denoted in the form of an exponential relationship if the ratio of the final value and the initial value can be represented by a power of the Euler's Constant which is denoted by the number e. In this case, we mul...
Modulo Class: The modulo class of a particular number for a specific modulo system pertains to the remainder when that number is divided by the number of the modulo system. That is, we have to perform division when determining the modulo class. ...
Prove that there are infinitely many primes with remainder of 3 when divided by 4. What is the number of 5-digit numbers that can be formed by the digits 0, 1, 2, 3, 4, 5 that are divisible by 5? Show that 5 divides n^5 - n for all integers. Consider all whole ...
Let r be a primitive root of the odd prime p. Prove the following: If p = 3 (mod4), then -r has order (p - 1)/2 modulo p. Using quadratic reciprocity find the primes for which 7 is a quadratic residue. Use fermat's theorem to find the remainde...