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Carmichael Numbers

›๋ฌธ๋ณด๊ธฐ
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ธ๊ธฐ๋„:B(A,B,C), „๊ณต๋ฅ :๋ณด†ต(๋‚ฎŒ,๋ณด†ต,๋†’Œ), ๋ ˆ๋ฒจ:2(1~4)

About CarmichaelNumbers

•”˜ธ •Œ๊ณ ๋ฆฌฆ˜ ค‘—๋Š” ฐ †Œˆ˜๋ฅผ ™œšฉ•˜๋Š” ๊ฒƒ๋„ žˆ๋‹ค. •˜ง€๋งŒ –ด๋–ค ฐ ˆ˜๊ฐ€ †Œˆ˜ธง€๋ฅผ Œ๋‹จ•˜๋Š” ๊ฒƒ€ ๊ทธ๋ฆฌ ‰ฝง€ •Š๋‹ค.
Ž˜๋ฅด๋งˆ …ŒŠคŠธ™€ ๊ฐ™ด ๋น ๋ฅธ †๋„๋กœ ๋งคšฐ  •™••˜๊ฒŒ †Œˆ˜ —ฌ๋ถ€๋ฅผ Œ๋‹จ•  ˆ˜ žˆ๋Š” ™•๋ฅ   †Œˆ˜ …ŒŠคŠธ ๋ฐฉ๋ฒ•ด๋ผ๋Š” ๊ฒƒด žˆ๋‹ค. †Œˆ˜ —ฌ๋ถ€๋ฅผ Œ๋‹จ•ด•ผ •   •ˆ˜ nด ฃผ–ดกŒ„ ๋•Œ a๋Š” 2ดƒ n-1ด•˜˜ ๋‚œˆ˜๋ผ๊ณ  •˜ž. ๊ทธ๋Ÿฌ๋ฉด ๋‹คŒ๊ณผ ๊ฐ™€ ‹ด „๋ฆฝ•˜๋ฉด n€ †Œˆ˜ผ ๊ฐ€๋Šฅ„ด žˆ๋‹ค.

a^n mod n = a

–ด๋–ค  •ˆ˜๊ฐ€ ด๋Ÿฌ•œ Ž˜๋ฅด๋งˆ …ŒŠคŠธ๋ฅผ —ฌ๋Ÿฌ ๋ฒˆ †ต๊ณผ•˜๋ฉด ๊ทธ  •ˆ˜๋Š” †Œˆ˜ผ ๊ฐ€๋Šฅ„ด ๋†’๋‹ค๊ณ  •  ˆ˜ žˆ๋‹ค. •˜ง€๋งŒ •ˆ ข‹€ †Œ‹๋„ žˆ๋‹ค. •ฉ„ˆ˜(†Œˆ˜๊ฐ€ •„๋‹Œ ˆ˜) ค‘—๋Š” ๊ทธ ˆ˜๋ณด๋‹ค ž‘€ ๋ชจ๋“   •ˆ˜— ๋Œ€•ด ด Ž˜๋ฅด๋งˆ …ŒŠคŠธ๋ฅผ †ต๊ณผ•˜๋Š” ๊ฒƒ๋„ žˆ๋‹ค. ด๋Ÿฐ ˆ˜๋ฅผ นด๋งˆดด ˆ˜๋ผ๊ณ  ๋ถ€๋ฅธ๋‹ค.

ฃผ–ด„  •ˆ˜๊ฐ€ นด๋งˆดด ˆ˜ธง€ …ŒŠคŠธ•˜๊ธฐ œ„•œ ”„๋กœ๊ทธ๋žจ„ ๋งŒ๋“ค–ด๋ผ.

Input

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

Output

ž…๋ ฅ๋œ ๊ฐ ˆ˜— ๋Œ€•ด •„๋ž˜— žˆ๋Š” ถœ๋ ฅ ˜ˆ— ๋‚˜™€žˆ๋Š” ‹œผ๋กœ ๊ทธ ˆ˜๊ฐ€ นด๋งˆดด ˆ˜ธง€ •„๋‹Œง€๋ฅผ Œ๋‹จ•œ ๊ฒฐ๊ณผ๋ฅผ ถœ๋ ฅ•˜๋ผ.

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 ๊ฐœ๋ฐœ‹œ๊ฐ„ ฝ”๋“œ
๋ฌธ๋ณดฐฝ C++ 3h 30m CarmichaelNumbers/๋ฌธ๋ณดฐฝ
กฐ˜„ƒœ C . CarmichaelNumbers/กฐ˜„ƒœ

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