Problem $9-$ Bonus points $($

Ramanujan Number

$)$

Srinivasa Ramanujan

was an Indian mathematician who became famous for his intu$-$

ition for numbers. When the English mathematician

G$.$ H$.$ Hardy

came to visit him one

day,

Hardy

remarked that the number of his taxi was

$1729$

$,$ a rather dull number. To

which

Ramanujan

replied,

$$No$,$ Hardy! It is a very interesting number. It is

the smallest number expressible as the sum of two cubes in two different ways$$

$.$

Verify this claim by writing a program named

ramanujan.cpp

that accepts

n

$($int$)$ from

command$-$line arguments and writes to standard output all integers less than or equal to

n

that can be expressed as the sum of two cubes in two different ways. In other words, find

distinct positive integers

a$,$ b$,$ c

$,$ and

d

such that

a

$3$

$+$

b

$3$

$=$

c

$3$

$+$

d

$3$

$$

n

$.$

Your program should report the message

$$Invalid value of n$$

if

n

$$

$0$

$/$workspace$/$csc$117/$hw$7$

$\%$ g$++-$o out$/$ramanujan$.$out src$/$ramanujan$.$cpp

$\%./$out$/$ramanujan$.$out $30000$

$1729=1^3+12^3=9^3+10^3$

$4104=2^3+16^3=9^3+15^3$

$6$

$13832=2^3+24^3=18^3+20^3$

$20683=10^3+27^3=19^3+24^3$

$\%./$out$/$ramanujan$.$out $-10000$

Invalid value of N

Hins:

$$

Use four nested

for

loops with these bounds on the loops variables: $0$

$<$ a

$$

$3$

$$

n

$,$

a $<$ b

$$

$3$

$$

n

$$

a

$3$

$,$

a $<$ c

$$

$3$

$$

n

$,$ and

c $<$ d

$$

$3$

$$

n

$$

c

$3$

$.$

$$

Do not explicitly compute cube roots use

x$*$x$*$x $<$ y

instead of using

x $<$ cbrt$($y$)$