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Home Q & A Board Science-Related Homework Help Mathematics
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otter1202 otter1202
wrote...
11 years ago
D=(396K+1)/151.  K can be any number but D must be an integer. The only value for K that makes D an integer is K=53. Is their a way to find K other than trial and error(trying different values for K until you get an integer)?
Thanks in advance to the genius who can answer this.
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nygard93 Author
wrote...
#1
11 years ago
There are infinity solutions to this. D can be ANY integer.
151D = 396K + 1
151D - 1 = 396K
K = (151D - 1) / 396

If D = 0 then K = -1/396
If D = 1 then K = 25/66 =~ 0.3787878...
If D = 2 then K = 301/396 =~ 0.76010101...
etc.

However, if you want both D and K to be integers, most of those solutions don't work, but there are still infinity solutions:
If D = 139 then K = 53
If D = 535 then K = 204
If D = 931 then K = 355
etc.
Once you find one solution, the rest are easy to find: just add 396 to D and 151 to K.
wrote...
#2
11 years ago
If D must be an integer but K can be any number, solve for K:

D=(396K+1)/151 becomes

K = (151D - 1) / 396

Now you can find many values for K by setting D = any integer

D=-2  Rightwards Arrow  K=-303/396
D=0  Rightwards Arrow  K=-1/396
D=5  Rightwards Arrow  K=754/396
D=139  Rightwards Arrow  K=53
Etc.
nygard93 Author
wrote...
#3
11 years ago
D=(396K+1)/151 --->(396K+1)=151*D ------->396K =151D-1
                                                                K= (151D-1)/396
                         so K has many options for D being a positive or negative integer
   D          K
  -3      -1,1414
  -2      -0,7601
  -1      -0,3788
   0       0,0025
   1       0,3838
   2       0,7652
   3       1,1465
wrote...
#4
11 years ago
D=(396k+1)/151=>
396k=-1(mod 151)=>
396=150(mod 151)=>
198k=75(mod 151)=>
k=3375(mod 151)=>
k=3375-22*151(mod 151)=>
k=53(mod 151)
So, k=53.
wrote...
#5
11 years ago
It seems to me like you always have to do trial and error the way i see it is like this in your example
d=396.53/151        then  d=138.9934
if we take the integer part  then
i part[138.9934]  is 138.0000 is the integer part with out +1
if we take full integer then  we have
int (396.53+1) /151      then we get full integer value of 139.0000  all of this of course is with k=53  the rest
i don't know good luck
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