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Carmichael Numbers

›ฌธณดธฐ
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ธธฐ„:B(A,B,C), „ณตฅ :ณดํ†ต(‚ฎŒ,ณดํ†ต,†’Œ),  ˆฒจ:2(1~4)

About CarmichaelNumbers

•”ํ˜ธ •Œณ ฆฌฆ˜ ค‘—Š” ํฐ †Œˆ˜ ํ™œšฉํ•˜Š” ฒƒ„ žˆ‹ค. ํ•˜€งŒ –ด–ค ํฐ ˆ˜€ †Œˆ˜ธ€ ํŒ‹จํ•˜Š” ฒƒ€ ทธฆฌ ‰ฝ€ •Š‹ค.
ํŽ˜ฅดงˆ ํ…ŒŠคํŠธ™€ ฐ™ด  ฅธ †„กœ งคšฐ  •ํ™•ํ•˜ฒŒ †Œˆ˜ —ฌ€ ํŒ‹จํ•  ˆ˜ žˆŠ” ํ™•ฅ   †Œˆ˜ ํ…ŒŠคํŠธ ฐฉฒ•ดŠ” ฒƒด žˆ‹ค. †Œˆ˜ —ฌ€ ํŒ‹จํ•ด• ํ•   •ˆ˜ nด –ดกŒ„ •Œ aŠ” 2ดƒ n-1ดํ•˜˜ ‚œˆ˜ณ  ํ•˜ž. ทธŸฌฉด ‹คŒ ฐ™€ ‹ด „ฆฝํ•˜ฉด n€ †Œˆ˜ €Šฅ„ด žˆ‹ค.

a^n mod n = a

–ด–ค  •ˆ˜€ ดŸฌํ•œ ํŽ˜ฅดงˆ ํ…ŒŠคํŠธ —ฌŸฌ ฒˆ ํ†ตํ•˜ฉด ทธ  •ˆ˜Š” †Œˆ˜ €Šฅ„ด †’‹คณ  ํ•  ˆ˜ žˆ‹ค. ํ•˜€งŒ •ˆ ข‹€ †Œ‹„ žˆ‹ค. ํ•ฉ„ˆ˜(†Œˆ˜€ •„‹Œ ˆ˜) ค‘—Š” ทธ ˆ˜ณด‹ค ž‘€ ชจ“   •ˆ˜— Œ€ํ•ด ด ํŽ˜ฅดงˆ ํ…ŒŠคํŠธ ํ†ตํ•˜Š” ฒƒ„ žˆ‹ค. ดŸฐ ˆ˜ งˆดํด ˆ˜ณ  €ฅธ‹ค.

–ด„  •ˆ˜€ งˆดํด ˆ˜ธ€ ํ…ŒŠคํŠธํ•˜ธฐ œ„ํ•œ ํ”„กœทธžจ„ งŒ“ค–ด.

Input

ž… ฅ€ —ฌŸฌ „กœ ตฌ„˜ฉฐ ฐ „—Š” ž‘€ –‘˜  •ˆ˜ n(2

Output

ž… ฅœ ฐ ˆ˜— Œ€ํ•ด •„ž˜— žˆŠ” ถœ ฅ ˜ˆ— ‚˜™€žˆŠ” ‹œกœ ทธ ˆ˜€ งˆดํด ˆ˜ธ€ •„‹Œ€ ํŒ‹จํ•œ ฒฐ ถœ ฅํ•˜.

Sample Input

~cpp 
1729
17
561
1109
431
0

Sample Output

~cpp 
The number 1729 is a Carmichael number.
17 is normal.
The number 561 is a Carmichael number.
1109 is normal.
431 is normal.

ํ’€ด

ž‘„ž ‚ฌšฉ–ธ–ด ฐœฐœ‹œ„ ฝ”“œ
ฌธณดฐฝ C++ 3h 30m CarmichaelNumbers/ฌธณดฐฝ
กฐํ˜„ํƒœ C . CarmichaelNumbers/กฐํ˜„ํƒœ

“ฐ ˆ“œ

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