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It is divisible by 3 and by 8. [6] 552: it is divisible by 3 and by 8. 25: The last two digits are 00, 25, 50 or 75. 134,250: 50 is divisible by 25. 26: It is divisible by 2 and by 13. [6] 156: it is divisible by 2 and by 13. Subtracting 5 times the last digit from 2 times the rest of the number gives a multiple of 26. (Works because 52 is ...
The first thousand values of φ(n).The points on the top line represent φ(p) when p is a prime number, which is p − 1. [1]In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n.
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
For example, (24 / 6) / 2 = 2, but 24 / (6 / 2) = 8 (where the use of parentheses indicates that the operations inside parentheses are performed before the operations outside parentheses). Division is traditionally considered as left-associative. That is, if there are multiple divisions in a row, the order of calculation goes from left to right ...
The eight divisors counted by this formula are 1, 2, 4, 8, 3, 6, 12, and 24. ... and that the Riemann hypothesis is equivalent to the inequality just for n divisible ...
a ≡ 1 (mod 4) if n is divisible by 4 but not 8; or a ≡ 1 (mod 8) if n is divisible by 8. Note: This theorem essentially requires that the factorization of n is known. Also notice that if gcd(a,n) = m, then the congruence can be reduced to a/m ≡ x 2 /m (mod n/m), but then this takes the problem away from quadratic residues (unless m is a ...
Squares of even numbers are even, and are divisible by 4, since (2n) 2 = 4n 2. Squares of odd numbers are odd, and are congruent to 1 modulo 8, since (2n + 1) 2 = 4n(n + 1) + 1, and n(n + 1) is always even. In other words, all odd square numbers have a remainder of 1 when divided by 8. Every odd perfect square is a centered octagonal number ...
The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).