All Questions ⁺⁰236075 Questions

0

17

1

+622

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from read more ..

cooIcooIcooI17 Jul 7, 2024

0

17

0

+948

Algebra

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.

Rangcr897 Jul 7, 2024

0

16

1

+948

Algebra

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

Rangcr897 Jul 7, 2024

0

16

1

+948

Algebra

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

Rangcr897 Jul 7, 2024

0

12

2

+948

Algebra

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

Rangcr897 Jul 7, 2024

0

8

3

+118

Geometry - help

In parallelogram EFGH let M be the point on EF such that FM:ME = 1:2, and let N be the point on EH such that HN:NE = 1:3. Line segments FH and GM intersect at P and line segments FH and GN intersect at Q. Find PQ/FH

SilviaJendeukie Jul 7, 2024

0

22

0

+842

Number Theory

Find the number of solutions to
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{6}, \\
N &\equiv 2 \pmod{7}
in the interval 0 \le N < 1000.

RedDragonl Jul 7, 2024

0

18

0

+842

Number Theory

Find the number of solutions to
N &\equiv 2 \pmod{6}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{8}
in the interval 0 \le N < 1000.

RedDragonl Jul 7, 2024

0

9

1

+842

Number Theory

Brandon spends his afternoon picking apples from an orchard. He notices that if he groups the apples he picked by fives, six, or sevens, then he ends up with $1$ left over. If he groups by eights, he has $1$ left over. If Brandon read more ..

RedDragonl Jul 7, 2024

0

20

0

+842

Number Theory

John and Ling start their new jobs on the same day. John's schedule is six workdays followed by one day off. Ling's schedule is seven workdays followed by one day off. On how many days during their first year of work ($365$ days) read more ..

RedDragonl Jul 7, 2024

0

21

0

+842

Number Theory

When $N$ is divided by $10$, the remainder is $a$. When $N$ is divided by $2$, the remainder is $b$. What is $N$ modulo $20$, in terms of $a$ and $b$?

RedDragonl Jul 7, 2024

0

13

0

+842

Number Theory

An eccentric baseball card collector wants to distribute her collection among her descendants. If she divided her cards among her $13$ great-great-grandchildren, there would be $8$ cards left over. If she divided her cards among her $10$ great-grandchildren, read more ..

RedDragonl Jul 7, 2024

0

17

0

+842

Number Theory

Carlos wants to send Cecil a message encrypted with RSA. Cecil has published his public encryption exponent $3$ and his public modulus $3$. When Carlos encrypts the number $3$ with this system, what is the result?

RedDragonl Jul 7, 2024

0

34

0

+842

Number Theory

The House of Lilliput is using RSA encryption to receive secret messages from all the realms. They have published their public encoding exponent $e = 8$ and their public modulus $M = pq = 6$.
Break the code: Find their secret decoding read more ..

RedDragonl Jul 7, 2024

0

10

1

+1310

Number Theory

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{7}.

learnmgcat Jul 7, 2024

0

18

1

+1310

Number Theory

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{3}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{10}.

learnmgcat Jul 7, 2024

0

16

1

+1310

Number Theory

Find the smallest positive integer $N$ such that
N &\equiv 4 \pmod{6}, \\
N &\equiv 4 \pmod{10}, \\
N &\equiv 4 \pmod{15}, \\
N &\equiv 4 \pmod{24}.

learnmgcat Jul 7, 2024

0

11

1

+842

Number Theory

Find a six-digit multiple of $64$ that consists only of the digits $2$ and $4$.

RedDragonl Jul 7, 2024

0

12

1

+842

Number Theory

A school orders $99$ textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?
_18,486.7_

RedDragonl Jul 7, 2024

0

13

0

+842

Number Theory

Let $m$ and $n$ be non-negative integers. If $m = 6n + 2$, then what integer between $0$ and $m$ is the inverse of $5$ modulo $m$? Answer in terms of $n$.

RedDragonl Jul 7, 2024

0

22

1

+842

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?

RedDragonl Jul 7, 2024

0

8

1

+842

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?

RedDragonl Jul 7, 2024

0

12

2

+868

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

eramsby1O1O Jul 7, 2024

0

17

0

+868

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the largest number of primes that could divide a terrific positive integer?

eramsby1O1O Jul 7, 2024

0

12

1

+868

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

eramsby1O1O Jul 7, 2024

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