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And counting (Posted on 2019-02-28) Difficulty: 3 of 5
a + b + c = 3
a2 + b2 + c2 < 10
a3 + b3 + c3 = 15
a4 + b4 + c4 = 35
a5 + b5 + c5 = m

Find m.

No Solution Yet Submitted by Danish Ahmed Khan    
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Hunting via computer w/ no luck | Comment 1 of 4
I have a feeling there are complex numbers afoot, but
I could not find a set with integer real and imaginary parts. 

the following yields no answer:
program fff

        implicit none

        complex a,b,c,m,z2,z3,z4,z5,c3

        real ra,rb

        integer ira,irb,ia,ib

        c3=complex(3.,0.)

        do  ira=-150,150

        ra=ira

        do   irb=-150,150

        rb=irb

        do   ia=-150,150

        do 2  ib=-150,150

        a=complex(ra,1.*ia)

        b=complex(rb,1.*ib)

        c=c3-a-b

        z2=a**2+b**2+c**2

        if(aimag(z2).ne.0)go to 2

        z3=a**3+b**3+c**3

        if(aimag(z3).ne.0)go to 2

        z4=a**4+b**4+c**4

        if(aimag(z4).ne.0)go to 2

        z5=a**5+b**5+c**5

        if(real(z2).ge.10)go to 2

        if(real(z3).ne.15)go to 2

        if(real(z4).ne.35)go to 2

        m = a**5+b**5+c**5

        print*,m

2       enddo

        enddo

        enddo

        enddo

        end


Edited on February 28, 2019, 5:12 pm
  Posted by Steven Lord on 2019-02-28 17:11:29

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