GCD
Diophantine Equations
Encryption
Decryption
100

Find the greatest common divisor d of 897 and 559.

13

100

Find integers x and y solving the equation 

116x + 16y =GCD(116, 16)

x = 1 and y = -7

100

Encrypt the following message with a shift of +7 

Logic is the foundation of the certainty of all the knowledge we acquire

Svnpj pz aol mvbukhapvu vm aol jlyahpuaf vm hss aol ruvdslknl dl hjxbpyl

100

Decrypt this message encrypted using the Caesar Cipher. 


Vs V unir frra shegure guna bguref, vg vf ol fgnaqvat hcba gur fubhyqref bs tvnagf

If I have seen further than others, it is by standing upon the shoulders of giants (+13)

200

Find the greatest common divisor d of 201 and 84.

3

200

Find integers x and y solving the equation 

584x + 404y = GCD(584, 404)

x = 9 and y = -13

200

Encrypt the following message with affine key (21, 16)

The enchanting charms of this sublime science reveal themselves only to those who have the courage to go deeply into it

Zhw wdghqdzcdm ghqjie yr zhce eulnciw egcwdgw jwpwqn zhwiewnpwe ydna zy zhyew khy hqpw zhw gyujqmw zy my bwwtna cdzy cz

200

Decrypt this message, that was encrypted with Affine Key (7, 17)

Ul uolnt pol ml elu jelp xruotxruvfn vu vn mvaavfbqu ul htu rfglnn r gtrq attqveh rn ul uot ytrbud, uot mttstnu ytrbud, la erubgt

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature

300

Find the greatest common divisor d of 1929 and 135.

3

300

Find integers x and y solving the equation 

142x + 103y = GCD(142, 103).

x = 37 and y = -51

300

Encrypt the following message with rail fence cipher (4)

Just because we can’t find a solution it doesn’t mean that there isn’t one

JCEILINTETUEAWCFNOUNTSTNHHRNOSBUEATDSTODEMAATESNTSNAIOETIE

300

Decrypt this message that used the Rail fence Cipher

WMUSIBNYEHUBATTLKNSEESSMBALYNEEIIISGIEVNHPYUUAERBFLKAWYTOITHNTFRSUEHHNOI

Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful (5)

400

Find the greatest common divisor d of 332 and 87.

1

400

Find integers x and y solving the equation 

441x + 371y = GCD(441, 371)

x = 16 and y = -19

400

Use a columnar transposition cipher with a full rectangular array and keyword BACKFIRE to encrypt the following message:

Bottomless wonders spring from simple rules which are repeated without end

OSSORCEHBSSREIPTTWPMUHAOERFLHEIDONIIERETMDNMSEDETORSLATULEGPWRWN

400

Cryptanalyze the following message.  It was encrypted with a columnar transposition cipher using a full rectangular array. 

EAOOESMNGLSERSAOHFDNUIFMAOANNSTPSSHGOOAQTNRHNEIUEIXEETUTG

An equation for me has no meaning unless it expresses a thought of God

500

Find the greatest common divisor d of 34924 and 7117

1

500

Find integers x and y solving the equation 

1521x + 291y =GCD(1521, 291)

x = -22 and y = 115

500

Encrypt the following using the Vigenere Cipher with keyword ULTRA:


Discovery is something to be cherished.

Xtltoppkp im dhdensbeg nz uv cbpkzsbpw.

500

Decrypt this message, that was encrypted using the Vigenere Cipher

Yezhqqgtugy adi zhq vksgpz or qesfixiayy paakre aniol to ark uzhkrexgnpw, gnp aniol zhq ytcarycusas diiosrotust or fkagxe mgwz pxee az mspavzazx vadx.

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part.

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