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枫下家园 / 望子成龙 / 征寻数学才子,求解数学难题。不胜感激!Problem 1: For how many integer values of n, are both n and n+2004 perfect squares?
(a) 1, (b) 2, (c) 3, (d) 4, (e) 5.
Problem 2: If N, N+1 and N+2 are the smallest consecutive integers, greater than 10, such that the first is divisible by 7, the second by 8 and the last by 9, then
(a) 100<N<200, (b) 200<N<300, (c) 300<N<400, (d) 400<N<500, (e) 500<N<600,
Please give your solutions and explanations. Thank you very much.
-lilyflower(tiger);
2006-1-6
{431}
(#2702041@0)
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第二题n=7*8*9+7=511
-lisa2(乐了);
2006-1-10
(#2709225@0)
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Thanks a lot!
-lilyflower(tiger);
2006-1-10
(#2709536@0)
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Problem 1: cSuppose n + 2004 = x^2 +2004 = (x+a)(x+a)
so 2004 = a(2x+a). x and a are both integers.
2004 = 167 x 3 x 2 x 2 (167, 3, 2 are primes)
There is three solutions for 2004 = a(2x+a) where a = 2 or 6 or 12
-smallwhale(喝不了咖啡);
2006-1-10
{210}
(#2709238@0)
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Thank you very much!
-lilyflower(tiger);
2006-1-10
(#2709542@0)
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第1题:y*y-x*x=2004
y=x+m
(x+m)*(x+m)-x*x=2004
(2x+m)*m=2004
如果m为奇数,左边也为奇数,不成立
所以m=2a
(2x+2a)*2a=2004
(x+a)a=501
501=3*167或1*501
分别得出x=164,y=170或x=500,y=502
-helloyou(你好!QQ230);
2006-1-10
{182}
(#2709242@0)
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Thank you very much!
-lilyflower(tiger);
2006-1-10
(#2709545@0)