替换码解码后的文本

A mathematician, like a painter or a poet, is a maker of patterns.

If his patterns are more permanent than theirs, it is because they are made with ideas. The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

密码如表4-14所示。

表　4-14

a

b

c

d

e

f

g

h

i

j

k

l

M

明文

B

A

N

T

S

H

U

F

L

K

X

I

O(www.daowen.com)

n

o

p

q

r

s

t

u

v

w

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y

Z

密文

C

M

Q

P

V

E

D

G

R

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W

J

Y

一个简单的难题

答案是正面。13 068 221=3613×3617。3613和3617都是除以4余1的质数。有一种方式可以很快地把该数字分解开来，这是费马发现的一个方法。3615的平方是13 068 225，与我们所探求的数字相差4，而4也是一个平方数。这时可运用一个几何运算法则，a²-b²=(a+b)×(a-b)，由此可得出：

13 068 221=(3615)²-2²=(3615+2)×(3615-2)=3613×3617