Podcast
Questions and Answers
Which equation has a solution where $X = 170$ and $Y = 357?
Which equation has a solution where $X = 170$ and $Y = 357?
- $540X + 630Y = 270$
- $170X + 357 = 34$ (correct)
- $6630X + 7956Y = 1326$
- $23716X + 75460Y = 6468$
If $b$ divides the difference $r - s$, where $0 \leq r \leq b$ and $0 \leq s \leq b$, then what can be concluded about $r$ and $s?
If $b$ divides the difference $r - s$, where $0 \leq r \leq b$ and $0 \leq s \leq b$, then what can be concluded about $r$ and $s?
- $r$ and $s$ can be either equal or different
- $r$ and $s$ must be equal (correct)
- $r$ and $s$ must be different
- No conclusion can be drawn about the relationship between $r$ and $s
Let $a$, $b$, and $c$ be integers with $c \neq 0$. Which of the following statements is true?
Let $a$, $b$, and $c$ be integers with $c \neq 0$. Which of the following statements is true?
- $c$ divides $a - b$ if and only if $a$ and $b$ have different remainders after division by $c$
- $c$ divides $a - b$ if and only if $a$ and $b$ have the same remainder after division by $c$ (correct)
- $c$ divides $a - b$ if and only if $a$ and $b$ are both multiples of $c$
- $c$ divides $a - b$ if and only if $a$ and $b$ are both divisible by $c$
Let $a$, $b$, and $c$ be integers with $a$, $b$, $c \neq 0$ and $c \neq 0$. Which of the following is true about the greatest common divisor (GCD) of $ca$ and $cb$?
Let $a$, $b$, and $c$ be integers with $a$, $b$, $c \neq 0$ and $c \neq 0$. Which of the following is true about the greatest common divisor (GCD) of $ca$ and $cb$?
Which of the following equations is an example of a Diophantine equation?
Which of the following equations is an example of a Diophantine equation?
What is the relationship between the remainders of $a$ and $b$ after division by $c$, if $c$ divides $a - b$?
What is the relationship between the remainders of $a$ and $b$ after division by $c$, if $c$ divides $a - b$?
Which of the following statements about the greatest common divisor (GCD) of $ca$ and $cb$, where $a$, $b$, and $c$ are integers with $c \neq 0$, is false?
Which of the following statements about the greatest common divisor (GCD) of $ca$ and $cb$, where $a$, $b$, and $c$ are integers with $c \neq 0$, is false?
