 
 <prompt> text: ```For mathematics, modular arithmetic na system of arithmetic for integers, where numbers dey "wrap around" once dem reach one certain value - the modulus (plural moduli). The modern approach to modular arithmetic na Carl Friedrich Gauss develop am for im book "Disquisitiones Arithmeticae", wey dem publish for 1801.

One common use of modular arithmetic na for di 12-hour clock, where di day dey divide into two 12-hour periods. If time na 7:00 now, then 8 hours later e go be 3:00. Normal addition go suggest say di later time suppose be 11:00, but dis no be di correct answer because clock time dey "wrap around" every 12 hours. Because di hour number dey start again once e reach 12, dis na arithmetic "modulo" 12. According to di definition wey dey below, 12 dey congruent not only to 12 itself, but also to 0, so di time wey dem dey call "12:00" fit also be called "0:00", since 12 dey congruent to 0 modulo 12.

Modular arithmetic fit dey handle mathematically by introducing one congruence relation on top di integers wey dey compatible with di operations on top integers: addition, subtraction, and multiplication. For one positive integer , two numbers and dey talk say dem be ", if their difference na one integer multiple of (that be say, if dem get one integer wey fit make their difference). Dis congruence relation dey usually consider when and na integers, and e dey denoted (some authors dey use instead of ; for dis case, if dem no put the parentheses, e generally mean say "mod" dey denote di modulo operation, wey be say, say ).

Based on top di article and di list of answers wey dey follow, write one list of questions.

1. 12
2. divide into two 12-hour periods
3. Carl Friedrich Gauss
4. 1801.
5. Disquisitiones Arithmeticae",
6. Yes
7. 0
8. Three
9. clock time
10. For mathematics, modular arithmetic na system of arithmetic for integers,
11. For mathematics
12. No
13. numbers
14. 0:00
15. unknown
16. no
17. no
18. Modulo operation
19. no
20. Carl Friedrich Gauss

Numbered questions:``` <response>: ```1. How many hours dey for clock?
2. how dem dey divide day?
3. na who publish am?
4. When?
5. for which book?
6. 12 equal anything else?
7. Wetin?
8. Wetin be time 8 hours after 7?
9. wetin wrap around after 12 hours?
10. wetin be modular arithmetic?
11. for which study?
12. letters dey wrap around?
13. so wetin e mean?
14. Wetin 12:00 fit mean?
15. 3:00 equal 18:00?
16. the integers dey compatible?
17. the integer negative?
18. wetin mod mean?
19. E fit be any number?
20. who develop the modern tech?``` 