Lesson test: Modular arithmetic

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Modular arithmetic

1.[2p]
Using the alternating digit sum, what remainder does $8 712 392$ leave on division by $11$ ? Give a number from $0$ to $10$ .

CorrectNot quite: 7

2.[2p]
1 January 2026 fell on a Thursday. On what day of the week does 1 January 2030 fall? (2028 is a leap year.)

Monday

The answer is: Tuesday

Tuesday

Correct

Wednesday

The answer is: Tuesday

Thursday

The answer is: Tuesday

3.[2p]
Find the inverse of $17$ modulo $60$ , as a number from $0$ to $59$ .

CorrectNot quite: 53

4.[2p]
Which of these classes have a multiplicative inverse modulo $12$ ?

Select all that apply

$[2]$

The answer is: $[5]$, $[7]$, $[11]$

$[5]$

Correct

$[7]$

Correct

$[9]$

The answer is: $[5]$, $[7]$, $[11]$

$[11]$

Correct

5.[2p]
How many solutions modulo $90$ does $42 x \equiv 12 (mod 90)$ have?

CorrectNot quite: 6

6.[3p]
Find the smallest positive solution of $15 x \equiv 25 (mod 65)$ .

CorrectNot quite: 6

7.[3p]
Find the smallest positive $x$ with $x \equiv 2 (mod 5)$ , $x \equiv 3 (mod 7)$ and $x \equiv 4 (mod 9)$ .

CorrectNot quite: 157

8.[2p]
The first nine digits of the ISBN of the third edition of Knuth's The Art of Computer Programming, Volume 1, are 0-201-89683. What is the check digit?

CorrectNot quite: 4

9.[1p]
A clerk copies a valid ISBN-10. Which of these mistakes can the check digit fail to detect?

Changing one digit to a different digit

The answer is: Changing two different digits

Swapping two adjacent, different digits

The answer is: Changing two different digits

Changing two different digits

Correct

Changing the check digit alone

The answer is: Changing two different digits

0 / 19 points

Next lessonFermat, Euler and RSA

Made by Francisco.

1.[2p] Using the alternating digit sum, what remainder does 8712392 leave on division by 11? Give a number from 0 to 10.

2.[2p] 1 January 2026 fell on a Thursday. On what day of the week does 1 January 2030 fall? (2028 is a leap year.)

3.[2p] Find the inverse of 17 modulo 60, as a number from 0 to 59.

4.[2p] Which of these classes have a multiplicative inverse modulo 12?

5.[2p] How many solutions modulo 90 does 42x≡12(mod90) have?

6.[3p] Find the smallest positive solution of 15x≡25(mod65).

7.[3p] Find the smallest positive x with x≡2(mod5), x≡3(mod7) and x≡4(mod9).

8.[2p] The first nine digits of the ISBN of the third edition of Knuth's The Art of Computer Programming, Volume 1, are 0-201-89683. What is the check digit?

9.[1p] A clerk copies a valid ISBN-10. Which of these mistakes can the check digit fail to detect?

1.[2p]
Using the alternating digit sum, what remainder does $8 712 392$ leave on division by $11$ ? Give a number from $0$ to $10$ .

2.[2p]
1 January 2026 fell on a Thursday. On what day of the week does 1 January 2030 fall? (2028 is a leap year.)

3.[2p]
Find the inverse of $17$ modulo $60$ , as a number from $0$ to $59$ .

4.[2p]
Which of these classes have a multiplicative inverse modulo $12$ ?

5.[2p]
How many solutions modulo $90$ does $42 x \equiv 12 (mod 90)$ have?

6.[3p]
Find the smallest positive solution of $15 x \equiv 25 (mod 65)$ .

7.[3p]
Find the smallest positive $x$ with $x \equiv 2 (mod 5)$ , $x \equiv 3 (mod 7)$ and $x \equiv 4 (mod 9)$ .

8.[2p]
The first nine digits of the ISBN of the third edition of Knuth's The Art of Computer Programming, Volume 1, are 0-201-89683. What is the check digit?

9.[1p]
A clerk copies a valid ISBN-10. Which of these mistakes can the check digit fail to detect?