Reply To: Maths
#98066
So, is no-one up to the challenge?
Since this challenge has been out for a while now, here are some hints. All have been encrypted with the ROT47 cipher (I am using ROT47 rather than ROT13 because of the abundance of punctuation involved). Good luck!
[*I will use the acronym FLT throughout to mean Fermat’s Little Theorem, not Fermat’s Last Theorem! Even I can agree that the latter would be a bit much…]
HINT 0 (solutions)
%96 @?=J G2=F6 @7 W2[3[AX E92E H@C<D :D W[[aX]
HINT 1 (FLT)
u6C>2EVD {:EE=6 %96@C6> DE2E6D E92E[ 7@C 2?J AC:>6 A 2?5 :?E686C < 4@AC:>6 E@ A[ </WA\X 92D C6>2:?56C @? 5:G:5:?8 3J A] W~C </WA\Xl >@5 A]X |@C6 FD67F==J 7@C E9:D AC@3=6>[ :E 2=D@ >62?D E92E 7@C 2?J AC:>6 A 2?5 p}* :?E686C <[ 6 C6>2:?56C @? 5:G:5:?8 3J A] %9:D >62?D E92E H6 >2J C6A=246[ D2J[ 2/A 3J 2 :? E96 AC@3=6> 2?5 DE:== AC6D6CG6 E96 C6>2:?56C @? 5:G:5:?8 3J A]]]
HINT 2 (first steps)
pD 9:?E65 2E :? w:?E `[ FD6 u{% E@ >@5:7J E96 =67E\92?5 D:56 @7 E96 6IAC6DD:@?[ H9:=DE AC6D6CG:?8 :ED C6>2:?56C @? 5:G:5:?8 3J A] W%92E :D[ 4@?D:56C 3@E9 D:56D >@5 A]X
s65F46 E92E 2Z3l_ W>@5 AX[ @C E92E A 5:G:56D W2Z3X]
</pre>
<strong>HINT 3</strong> (bounds on a,b,a+b)
<pre>
w:?E a DE2E65 E92E A 5:G:56D 2Z3]
x7 Ala E96? H6 92G6 2/aZ3/ala[ H9:49 :D 62DJ E@ 4964<[ D@ 2DDF>6 Ama] }@E6 E92E A :D @55] {6E ?lWAZ`X^a]
(C:E6 ?/A 2?5 AP 2D 7@==@HD WG:6H :? 2 >@?@DA2465 7@?EXi
?/A l ,?Y?. Y ,?Y ? . Y ]]] Y , ? Y ? . Y ?
AP l ,YA. Y ,aYWA\X. Y ]]] Y ,W?\XYW?ZX. Y ? !C@G6 E92E 6249 @7 E96 3C24<6ED 7@C ?/A 2C6 =2C86C E92? E9@D6 7@C AP] w6?46[ D:?46 2/A k AP k ?/A[ 565F46 E92E 2klW?\`X] $:>:=2C=J D9@H 3klW?\`X[ 2?5 96?46 D9@H E92E 2Z3kA]
HINT 4 (final steps)
WpDDF>:?8 Ama 96C6]]]X w:?E a D2:5 E92E A 5:G:56D 2Z3] w:?E b D2:5 E92E 2Z3kA] 2 2?5 3 2C6 A@D:E:G6[ D@ H6 2=D@ 92G6 2Z3m_] s6C:G6 2 4@?EC25:4E:@?]