The number N has the following properties:
(a)It consists of 4 digits, each digit is a number
less than 7.
(b)It is a square of a certain number.
(c)If 3 is added to each digit, the resulting number
is also a square of a number.
find N
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tpesamguo

2007-08-20 09:47
數字N有下列特性：
(a)它是一個四位數，且每一位數都小於7.
(b)它是一個正整數的平方.
(c)如果它的各位數字都加3，則這個數也是一個正整數的平方.
求N

A:1156 (34×34)

解法: 34×34＋3333＝67×67

:-) :-P

tpesamguo

2007-08-20 10:40
a^2+3333=b^2
=>
b^ 2 - a^2=3333
(b+a)(b-a)=3333=3*11*101
=>

(1) b+a=3333 b-a=1
(2) b+a=1111 b-a=3
(3) b+a=303 b-a=11
(4) b+a=101 b-a=33

(1)=>b=1667 a=1666 不合(a平方為1109556)
(2)=>b=557 a=554 不合(a平方為306916)
(3)=>b=157 a=146 不 合(a平方為21316)
(4)=>b=67 a=34 (b平方為4489 a平方為1156)