All Questions ⁺⁰237754 Questions

0

34

1

+1524

Number Theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(191)$?

learnmgcat Jul 26, 2024

0

55

1

+972

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

Rangcr897 Jul 26, 2024

0

47

0

+972

Geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Rangcr897 Jul 26, 2024

0

39

3

+14

Geometry Help - 2 of 2

In quadrilateral , sides and are extended past B and C, respectively, to meet at point A.
If:
BD = 18
BC = 8 read more ..

CPhill ●●●

readyformathlearning Jul 26, 2024

0

51

2

+14

Geometry Help - 1 of 2

In triangle ABC, points D and F are on and E is on such that and . If AF = 7 and DF = 2, then what is BD?
Thank you guys!!

readyformathlearning Jul 26, 2024

0

34

1

+2730

number theory help

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(191)$?

NotThatSmart ●

LiIIiam0216 Jul 26, 2024

0

63

1

+2730

need help

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(1200)$?

LiIIiam0216 Jul 26, 2024

Jul 25, 2024

0

39

1

+2730

help me plz

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. What is the smallest possible value of $n?$

LiIIiam0216 Jul 25, 2024

0

53

1

+2730

help help

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. How many prime numbers are divisors of $n?$

LiIIiam0216 Jul 25, 2024

0

65

0

+2730

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $10$ positive divisors, $n$ has exactly $16$ positive divisors, and $mn$ has exactly $21$ positive divisors. How many divisors does $m^2 n^2$ have?

LiIIiam0216 Jul 25, 2024

0

30

1

+2730

Number Theory

Let $M$ be the least common multiple of $1,$ $2,$ $\dots,$ $12$, $13$, $14$, $15$, $16$. How many positive divisors does $M$ have?

LiIIiam0216 Jul 25, 2024

0

50

0

+2730

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $10$ positive divisors, $n$ has exactly $16$ positive divisors, and $mn$ has exactly $21$ positive divisors. How many divisors does $m^2 n^2$ have?

LiIIiam0216 Jul 25, 2024

0

62

0

+2730

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $10$ positive divisors, $n$ has exactly $16$ positive divisors, and $mn$ has exactly $21$ positive divisors. How many divisors does $m^2 n^2$ have?

LiIIiam0216 Jul 25, 2024

0

54

0

+2730

help me help

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{10}?$

LiIIiam0216 Jul 25, 2024

0

63

0

+2730

need help

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

LiIIiam0216 Jul 25, 2024

0

50

1

+2730

help help

Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.

LiIIiam0216 Jul 25, 2024

0

38

1

+2730

help me

The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?

LiIIiam0216 Jul 25, 2024

0

50

0

+2730

help with number theory

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$

LiIIiam0216 Jul 25, 2024

0

65

0

+2730

Need help

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.

LiIIiam0216 Jul 25, 2024

0

47

0

+2730

Help me plz

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.

LiIIiam0216 Jul 25, 2024

0

59

1

+2730

Need help

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 ..

LiIIiam0216 Jul 25, 2024

0

37

1

+363

Modulo help

Let and be non-negative integers. If , then what integer between and is the inverse of modulo ? Answer in terms of .

Lilliam0216 Jul 25, 2024

0

41

1

+2730

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 ..

LiIIiam0216 Jul 25, 2024

0

48

0

+2730

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 $b$?

LiIIiam0216 Jul 25, 2024

0

61

0

+750

help probability

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
Ace of spades
Ace of hearts
Ace of diamonds read more ..

siIviajendeukie Jul 25, 2024

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