Subject: Mathematics
Book: Maths Mastery
Fermat’s Little Theorem says that if p is prime and gcd(a,p)=1, then a^(p–1)≡1 (mod p). Euler’s theorem generalizes it, stating a^φ(n)≡1 (mod n) for gcd(a,n)=1. These reduce exponents in modular arithmetic. For example, to find 3^100 mod 11, note φ(11)=10, so 3^100 = (3^10)^(10) ≡1^(10)≡1 mod 11. Such exponentiation shortcuts appear in coding, cryptography (like RSA), or advanced number theory tasks. Familiarity with these theorems speeds up computations involving large powers mod n.
What is the value of x if log(x) + log(4) = log(32)?
View QuestionIf log(100) = 2 and log(10) = 1, what is log(1000)?
View QuestionIf a:b = 3:4 and b:c = 5:6, what is a:c?
View QuestionA number is increased by 20% and then decreased by 10%. What is the net change?
View QuestionWhat is the sum of all odd numbers from 1 to 99?
View QuestionA train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?
View QuestionIf the perimeter of a square is 36 cm, what is the length of its diagonal?
View QuestionIf 5x - 2 = 13, what is the value of x?
View QuestionIf x = 2 and y = 3, what is the value of (x^2 + y^2)?
View QuestionIf a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?
View Question