# Yannes

## 解答 0

• leung_po_chuen
2020-09-03 15:55:09
=(10-3)^2009 Hence the remainder is (-3)^2009 Therefore 3x = -(-3)^2010 = -(3)^2010
• Yannes
2020-09-03 15:59:08
Umm Sorry I don’t really understand
•  leung_po_chuen 2020-09-03 15:55:09
• =(10-3)^2009 Hence the remainder is (-3)^2009 Therefore 3x = -(-3)^2010 = -(3)^2010
• leung_po_chuen
2020-09-03 16:11:33
Sorry, I neglect one thing. Rewrite 7^2009 into (10-3)^2009 If we really express it like a polynomial, the last 2 terms will be (-3)^2009 and 10(-3*2009). The rest of the term should contain 100 as the factor. x= (-3)^2009+10(-3*2009) 3x = -(3)^2010 -90*2009
•  Yannes 2020-09-03 15:59:08
• Umm Sorry I don’t really understand
• 解數雜貨店
2020-09-03 19:42:02
Define R(n) = remainder of 7ⁿ÷100 7¹ = 7 ⇒ R(1) = 7 7² = 49 ⇒ R(2) = 49 7³ = 343 ⇒ R(3) = 43 7⁴ = 2401 ⇒ R(4) = 1 7⁵ = 16807 ⇒ R(5) = 7 = R(1) Observed that the last two digits repeat every 4 times R(2009) = R(2005) = ... = R(1) ∴ x = 7 and 3x = 21

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