Determine the minimum value of a nonnegative integer N, such that:
(20N)!
------
(N!)21
is NOT an integer.
Provide valid reasoning to support your answer.
Note: Computer program or spreadsheet assisted methodologies are welcome, but an analytical solution is preferred.
clearvars, clc
n=1;
num=sym(factorial(20));
denBase=sym(1);
frac=num/denBase;
tFrac=char(frac);
while ~contains(tFrac,'/')
for i=20*n+1:20*(n+1)
num=num*i;
end
n=n+1;
if mod(n,100)==0
disp(n)
end
denBase=denBase*n;
den=denBase^21;
frac=num/den;
tFrac=char(frac);
end
n
frac
n =
23
frac =
3334519512505206218134585119545009657256373612882882011847970102497132943157107326708939373081366782
7008768427412270677053377314305248567498089481992828779594684530309485976222503361294750356180462449
3271524399687940612526888120729651082889694737182168635924973944061076028339442663685112948755738603
0018142947426323247630375683688900550158974883697139084235043587382879818168961617954374534925369189
5439896939149418031870334250155236729286683578438384439395832786549959982936367046378797657420406661
6970307117836689990723882188800000000000000000000000000000/23
>>
Edited on May 17, 2023, 10:59 am
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Posted by Charlie
on 2023-05-17 10:56:12 |
computer solution -- Matlab
