Fermat`s Little Theorem and Chinese Remainder Theorem Solutions
... Therefore if (m, n) is a solution with n ≥ 2 so that 4|2n , then 4 must divide 3m −1 = 2n and the equation above indicates m must be even. This allows us to factor: (3m/2 + 1)(3m/2 − 1) = 2n . Thus: a) (3m/2 + 1) and (3m/2 − 1) are both powers of 2 b) (3m/2 + 1) − (3m/2 − 1) = 2 What powers of 2 hav ...
... Therefore if (m, n) is a solution with n ≥ 2 so that 4|2n , then 4 must divide 3m −1 = 2n and the equation above indicates m must be even. This allows us to factor: (3m/2 + 1)(3m/2 − 1) = 2n . Thus: a) (3m/2 + 1) and (3m/2 − 1) are both powers of 2 b) (3m/2 + 1) − (3m/2 − 1) = 2 What powers of 2 hav ...
Basic Maths
... § 1. Logarithms and exponentials (applications) Exponential and logistic population growth models Exponential decay of drug concentration in a patient's body Richter scale for earthquakes uses logarithm scale Decibel scale for the power of sound uses logarithm scale Source reference: LeVa ...
... § 1. Logarithms and exponentials (applications) Exponential and logistic population growth models Exponential decay of drug concentration in a patient's body Richter scale for earthquakes uses logarithm scale Decibel scale for the power of sound uses logarithm scale Source reference: LeVa ...
mathematics 1º eso - IES Miguel de Cervantes
... A natural number, a, is a factor of another number, b, if the division of b by a is exact. If a natural number can be expressed as a product of two natural numbers, then these numbers are called factors of that number. For example, 14 = 2 · 7 , so 2 and 7 are factors of 14 All the factors of a numbe ...
... A natural number, a, is a factor of another number, b, if the division of b by a is exact. If a natural number can be expressed as a product of two natural numbers, then these numbers are called factors of that number. For example, 14 = 2 · 7 , so 2 and 7 are factors of 14 All the factors of a numbe ...
Full text
... Theorem 7. If A is a nonzero escalator number, then there is some minimal W > 1 such that for each m > W , there is no escalator sequence with A = Am . Further, if A = uv where u, v ∈ Z, v > 0, then W ≤ v + 1. Proof. By Theorem 3, if An is any escalator number, then An ≤ 0 or An ≥ 4. Therefore, lett ...
... Theorem 7. If A is a nonzero escalator number, then there is some minimal W > 1 such that for each m > W , there is no escalator sequence with A = Am . Further, if A = uv where u, v ∈ Z, v > 0, then W ≤ v + 1. Proof. By Theorem 3, if An is any escalator number, then An ≤ 0 or An ≥ 4. Therefore, lett ...
the twin primes conjecture - some solutions
... infinite. (In fact, every odd number (in the infinite list of odd numbers) is either a prime number or a composite of prime numbers (i.e., it consists of prime factors), the primes being the “atoms” or building-blocks of the odd numbers (the primes could also be regarded as the building-blocks of al ...
... infinite. (In fact, every odd number (in the infinite list of odd numbers) is either a prime number or a composite of prime numbers (i.e., it consists of prime factors), the primes being the “atoms” or building-blocks of the odd numbers (the primes could also be regarded as the building-blocks of al ...
