Number Theory & Mathematical Logic Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Number Theory & Mathematical Logic flashcards as text
How many integers from 1 to 1000 are relatively prime to 1000?
Answer: 400
φ(1000) = 1000·(1/2)(4/5) = 400.
Which of the following CANNOT be written as a sum of two perfect squares?
Answer: 21
21 = 3·7 contains primes ≡ 3 (mod 4) to an odd power, while 13 = 4+9, 25 = 9+16, and 29 = 4+25.
What is the smallest integer n > 1 that leaves remainder 1 when divided by each of 2, 3, 4, 5, and 6?
Answer: 61
n − 1 must be a multiple of lcm(2,3,4,5,6) = 60, so n = 61.
How many trailing zeros does 2026! have?
Answer: 505
405 + 81 + 16 + 3 = 505 factors of 5.
The conditional statement P → Q is false exactly when:
Answer: P is true and Q is false
An implication fails only when a true hypothesis leads to a false conclusion.
What is the remainder when 2^2026 is divided by 9?
Answer: 7
2^6 ≡ 1 (mod 9) and 2026 ≡ 4 (mod 6), so 2^2026 ≡ 2^4 = 16 ≡ 7 (mod 9).
Which of the following is a perfect number?
Answer: 28
The proper divisors of 28 are 1+2+4+7+14 = 28.
How this page was made: written with AI tools. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy
Sources & references
Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy