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2007-05-13, 21:14
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#1 |
May 2004
New York City
23×232 Posts |
Divisible by 7
Show that 22225555 + 55552222 is divisible by 7.
More generally, when is ab + ba prime? (This part I don't have a completely general answer to.) |
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2007-05-13, 22:05
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#2 |
"Nancy"
Aug 2002
Alexandria
2,467 Posts |
2222 - 2100 = 122, 122 - 70 = 52, 52 - 49 = 3, so 2222%7 = 3. 3^6 == 1 (mod 7), 5555 - 4800 = 755, 755 - 720 = 35, 35 - 30 = 5, so 5555%6 = 5. 2222^5555 = 3^5 == 5 (mod 7). (The mod reduction is a bit long-winded, but I wanted to do this without electronic aid)
Same for 5555^2222 == 4^2 == 2 (mod 7). 5 + 2 == 0 (mod 7) Iirc, Paul Leyland has something to say about the more general question. Alex Last fiddled with by akruppa on 2007-06-04 at 15:51 Reason: fixed /spoiler |
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2007-05-14, 07:44
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#3 | |
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Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3·3,529 Posts |
Quote:
Note that site badly needs updating with more results sent to me relatively recently. Paul |
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2007-05-14, 22:05
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#4 |
Nov 2005
2×7×13 Posts |
Yeah, it's pretty clear that you use the properties of modulas and exponentiation together.
Last fiddled with by nibble4bits on 2007-05-14 at 22:05 |
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