Çözüldü EBOB - EKOK - Programlama

a·b = EKOK(a, b) · EBOB(a, b) = 25·9a = 25·8b
a·b = 25·9a ---> b = 25·9
a·b = 25·8b ---> a = 25·8 ---> a + b = 25(9 + 8) = 25·17 = 425

Fortran çözümü:

https://i.ibb.co/dJ58f2gh/a-b-Fortran.png

Program:

Kod:

! a ve b doğal sayılardır. EBOB(a, b) = 25 ve EKOK(a, b) = 9a = 8b ise a + b = ?
program a_b
integer :: ax, bx, lcm, gcd

do ax = 1, 500; do bx = 1, 500

   if ((gcd(ax, bx) == 25).and.(lcm(ax, bx) == 9*ax).and.              &
      (lcm(ax, bx) == 8*bx).and.(9*ax == 8*bx)) print*,ax+bx

enddo; enddo

end

!Modified version of https://rosettacode.org/wiki/Least_common_multiple#Fortran
integer function lcm(a,b)
integer:: a,b,gcd
lcm = a*b / gcd(a,b)
end function lcm

!https://rosettacode.org/wiki/Greatest_common_divisor#Iterative_Euclid_algorithm_3
integer function gcd(v,t)
integer, intent(in) :: v, t
integer :: c, b, a
b = t
a = v
do
  c = mod(a, b)
  if (c == 0) exit
  a = b
  b = c
end do

gcd = b
 
end function gcd