#include <stdio.h>
typedef unsigned long long ULL;
void f(int n,ULL *a, ULL *b){
	int i = 0;
	ULL t;
	*a = 1;
	*b = 1;
	while(n>>i>1) i++;
	while(i--){
		t = *a;
		*a = t*t+5**b**b;
		*b = 2*t* *b;
		if(1<<i&n){
			t = *a;
			*a = t+5**b;
			*b = t+*b;
		}
	}
}
int main(void){
	int n;
	ULL a,b;
	for(n=1;n<100;n++){
		f(n,&a,&b);
		printf("(1+√(5))^%d = %llu + %llu√(5)\n",n,a,b);
	}
	return 0;
}

(1+√(5))^1 = 1 + 1√(5)
(1+√(5))^2 = 6 + 2√(5)
(1+√(5))^3 = 16 + 8√(5)
(1+√(5))^4 = 56 + 24√(5)
(1+√(5))^5 = 176 + 80√(5)
(1+√(5))^6 = 576 + 256√(5)
(1+√(5))^7 = 1856 + 832√(5)
(1+√(5))^8 = 6016 + 2688√(5)
(1+√(5))^9 = 19456 + 8704√(5)
(1+√(5))^10 = 62976 + 28160√(5)
(1+√(5))^11 = 203776 + 91136√(5)
(1+√(5))^12 = 659456 + 294912√(5)
(1+√(5))^13 = 2134016 + 954368√(5)
(1+√(5))^14 = 6905856 + 3088384√(5)
(1+√(5))^15 = 22347776 + 9994240√(5)
(1+√(5))^16 = 72318976 + 32342016√(5)
(1+√(5))^17 = 234029056 + 104660992√(5)
(1+√(5))^18 = 757334016 + 338690048√(5)
(1+√(5))^19 = 2450784256 + 1096024064√(5)
(1+√(5))^20 = 7930904576 + 3546808320√(5)
(1+√(5))^21 = 25664946176 + 11477712896√(5)
(1+√(5))^22 = 83053510656 + 37142659072√(5)
(1+√(5))^23 = 268766806016 + 120196169728√(5)
(1+√(5))^24 = 869747654656 + 388962975744√(5)
(1+√(5))^25 = 2814562533376 + 1258710630400√(5)
(1+√(5))^26 = 9108115685376 + 4073273163776√(5)
(1+√(5))^27 = 29474481504256 + 13181388849152√(5)
(1+√(5))^28 = 95381425750016 + 42655870353408√(5)
(1+√(5))^29 = 308660777517056 + 138037296103424√(5)
(1+√(5))^30 = 998847258034176 + 446698073620480√(5)
(1+√(5))^31 = 3232337626136576 + 1445545331654656√(5)
(1+√(5))^32 = 10460064284409856 + 4677882957791232√(5)
(1+√(5))^33 = 33849479073366016 + 15137947242201088√(5)
(1+√(5))^34 = 109539215284371456 + 48987426315567104√(5)
(1+√(5))^35 = 354476346862206976 + 158526641599938560√(5)
(1+√(5))^36 = 1147109554861899776 + 513002988462145536√(5)
(1+√(5))^37 = 3712124497172627456 + 1660112543324045312√(5)
(1+√(5))^38 = 12012687213792854016 + 5372237040496672768√(5)
(1+√(5))^39 = 1980384268857114624 + 17384924254289526784√(5)
(1+√(5))^40 = 15118029245466542080 + 918564449437089792√(5)
(1+√(5))^41 = 1264107418942439424 + 16036593694903631872√(5)
(1+√(5))^42 = 7660099598622392320 + 17300701113846071296√(5)
(1+√(5))^43 = 1929884799304990720 + 6514056638758912000√(5)
(1+√(5))^44 = 16053423919389999104 + 8443941438063902720√(5)
(1+√(5))^45 = 2932898888580857856 + 6050621283744350208√(5)
(1+√(5))^46 = 14739261233593057280 + 8983520172325208064√(5)
(1+√(5))^47 = 4316629874090442752 + 5276037332208713728√(5)
(1+√(5))^48 = 12250072461424459776 + 9592667206299156480√(5)
(1+√(5))^49 = 4873176271791587328 + 3395995594014064640√(5)
(1+√(5))^50 = 3406410168152358912 + 8269171865805651968√(5)
(1+√(5))^51 = 7858781349761515520 + 11675582033958010880√(5)
(1+√(5))^52 = 10896459298422915072 + 1087619310009974784√(5)
(1+√(5))^53 = 16334555848472788992 + 11984078608432889856√(5)
(1+√(5))^54 = 2467972595799031808 + 9871890383196127232√(5)
(1+√(5))^55 = 14933936364360564736 + 12339862978995159040√(5)
(1+√(5))^56 = 2846274964498153472 + 8827055269646172160√(5)
(1+√(5))^57 = 10088063165309911040 + 11673330234144325632√(5)
(1+√(5))^58 = 13114482114902884352 + 3314649325744685056√(5)
(1+√(5))^59 = 11240984669916758016 + 16429131440647569408√(5)
(1+√(5))^60 = 1152921504606846976 + 9223372036854775808√(5)
(1+√(5))^61 = 10376293541461622784 + 10376293541461622784√(5)
(1+√(5))^62 = 6917529027641081856 + 2305843009213693952√(5)
(1+√(5))^63 = 0 + 9223372036854775808√(5)
(1+√(5))^64 = 9223372036854775808 + 9223372036854775808√(5)
(1+√(5))^65 = 0 + 0√(5)
(1+√(5))^66 = 0 + 0√(5)
(1+√(5))^67 = 0 + 0√(5)
(1+√(5))^68 = 0 + 0√(5)
(1+√(5))^69 = 0 + 0√(5)
(1+√(5))^70 = 0 + 0√(5)
(1+√(5))^71 = 0 + 0√(5)
(1+√(5))^72 = 0 + 0√(5)
(1+√(5))^73 = 0 + 0√(5)
(1+√(5))^74 = 0 + 0√(5)
(1+√(5))^75 = 0 + 0√(5)
(1+√(5))^76 = 0 + 0√(5)
(1+√(5))^77 = 0 + 0√(5)
(1+√(5))^78 = 0 + 0√(5)
(1+√(5))^79 = 0 + 0√(5)
(1+√(5))^80 = 0 + 0√(5)
(1+√(5))^81 = 0 + 0√(5)
(1+√(5))^82 = 0 + 0√(5)
(1+√(5))^83 = 0 + 0√(5)
(1+√(5))^84 = 0 + 0√(5)
(1+√(5))^85 = 0 + 0√(5)
(1+√(5))^86 = 0 + 0√(5)
(1+√(5))^87 = 0 + 0√(5)
(1+√(5))^88 = 0 + 0√(5)
(1+√(5))^89 = 0 + 0√(5)
(1+√(5))^90 = 0 + 0√(5)
(1+√(5))^91 = 0 + 0√(5)
(1+√(5))^92 = 0 + 0√(5)
(1+√(5))^93 = 0 + 0√(5)
(1+√(5))^94 = 0 + 0√(5)
(1+√(5))^95 = 0 + 0√(5)
(1+√(5))^96 = 0 + 0√(5)
(1+√(5))^97 = 0 + 0√(5)
(1+√(5))^98 = 0 + 0√(5)
(1+√(5))^99 = 0 + 0√(5)