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 HCF of 48 and 180?
View QuestionA triangle has angles 60°, 60°, and 60°. What type of triangle is it?
View QuestionWhat is the sum of the first 10 positive even numbers?
View QuestionWhat is the greatest common divisor (GCD) of 36 and 48?
View QuestionIf x^2 - 6x + 9 = 0, what is the value of x?
View QuestionIf the sum of three consecutive integers is 72, what are the integers?
View QuestionIf the perimeter of a square is 40 cm, what is the area of the square?
View QuestionThe sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?
View QuestionIf a:b = 7:9 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?
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