MEMEG0D

60 Questions
1 Answers

0

2

2

+238

Number Theory

Carl writes eight consecutive three-digit numbers on a blackboard. Each number that Carl writes is divisible by 2, 3, 4, or 5. What is the sum of the digits of the smallest number that Carl wrote?

MEMEG0D Oct 30, 2024

0

2

2

+238

Number Theory

When a prime is divided by 60, the remainder is a composite number. When a second prime is divided by 60, the remainder is a prime. Find the smallest possible value of the second prime.

MEMEG0D Oct 30, 2024

0

2

1

+238

Number Theory

How many three-digit numbers are equal to five times the sum of their digits?

MEMEG0D Oct 30, 2024

0

3

0

+238

Number Theory

A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are 2, $F$, and 1. If the integer is a multiple of $19_{10}$, what is the units digit?

MEMEG0D Oct 29, 2024

0

2

1

+238

Number Theory

The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?

MEMEG0D Oct 29, 2024

0

3

0

+238

Number Theory

Which of the residues 0, 1, 2, ..., 11 satisfy the congruence 3x = 1 mod 12?

MEMEG0D Oct 29, 2024

0

3

0

+238

Number Theory

Which of the residues 0, 1, 2, 3, 4 satisfy the congruence x^5 = 0 mod 5?

MEMEG0D Oct 29, 2024

+1

3

0

+238

Number Theory

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

MEMEG0D Oct 28, 2024

0

2

0

+238

Number Theory

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

MEMEG0D Oct 28, 2024

0

2

0

+238

Number Theory

What is the largest positive integer $n$ such that $1457$, $1797$, $709$, $15$, $24$, $197$, $428$ all leave the same remainder when divided by $n$?

MEMEG0D Oct 28, 2024