scala - power and modulo on the fly for big numbers -

I increase some base b into power p and take modules about it.

Suppose that B = 55170 or 55172 and m = 3043839241 (which is the square of 55171) gives the Linux calculator BC result (we need it for control) :

  echo "p = 5606; b = 55171; m = b * b; (b -1) ^ p)% m; (b + 1) ^ p)% m "| BC 2734550616 30 9 288627 Now the calculation of 55170 ^ 5606 now gives a large number to a large extent, but since I have to do a modulopressation, then I can dismiss the use of Biggunt, I thought, because  < / Pre> 
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  (a * b)% c == ((a% c) * (b% c))% c i.e. (9 * 7)% 5 == (( 9% 5) * (7% 5))% 5 = & gt; 63% 5 == (4 * 2)% 5 = & gt; 3 == 8% 5  
 
 ... and a ^ d = a ^ (b + c) = a ^ b * a ^ c, so i divided by b + c 2 I can calculate 8 ^ 2 * 8 ^ 3 for 8 ^ 5, for whatever or odd DSD / 2 and D- (D / 2), 
 
 So my (defective) method, which separates the separator on the fly, always looks like this: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ): Long = {if (pot == 1) B% mode other {Vial port 2 = pot / 2 wal 1 mm = powmod (b, pt2, md) val 2b I = 2 POWMODODE (B, POT-ST2, MD) (1 * Pm2)% mod}}  

and has been fed with some values,

  Povmod (55170, 5606, 3043839241) res2: lang = 1885539617 powmode (55172, 5606, 3043839241 l) res4: lang = 309288627  

As we can see, the second The result is very similar to the top, but the first looks a calm. I count such a lot, and as long as they live in the category of int, they seem accurate, but I do not see any error but also works by using a BigInt, but this is very much Slow down:

  def calc2 (n: int, pri: long) = {val p: BigInt = pri val p3 = p * p val p1 = (P -1) .p (n )% (P3) Val P2 = (P + 1). Po (N)% (P3) Print ("P1:" + P1 + "P2:" + P2)} Calculator (5606, 55171) p. 1: 2734550616 p2: 309288627  

(The result with BC) can anyone see the error in powMod ?