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How many positive integers N from 1 to 5000 satisfy the congruence \(N \equiv 11 \pmod{13}?\)

 Apr 27, 2019
 #1
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n=1;m=5000; c=0;a=if(n % 13==11, goto4,goto5);c=c+1;n++;if(n<5000, goto3, discard=0;print"Total = ",c

Total =  384

 Apr 28, 2019
 #2
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\(N \equiv 11 \pmod{13}? \qquad 1\le N \le 5000\\ \)

The first one is 11, the second is 13+11,  the kth one is (k-1)*13 +11 

5000/13 = 384.6153846153846154

384*13 = 4992

So the biggest one is  (383)*13+11 = 4990  

N-1=383

N=384

 Apr 28, 2019

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