Integer Diophantine equations solver

The equations have the following integer solutions:
6 = a+b+c

Number of solutions found: 210
a1=1, b1=-7, c1=12
a2=1, b2=-6, c2=11
a3=1, b3=-5, c3=10
a4=1, b4=-4, c4=9
a5=1, b5=-3, c5=8
a6=1, b6=-2, c6=7
a7=1, b7=-1, c7=6
a8=1, b8=0, c8=5
a9=1, b9=1, c9=4
a10=1, b10=2, c10=3
a11=1, b11=3, c11=2
a12=1, b12=4, c12=1
a13=1, b13=5, c13=0
a14=1, b14=6, c14=-1
a15=1, b15=7, c15=-2
a16=1, b16=8, c16=-3
a17=1, b17=9, c17=-4
a18=1, b18=10, c18=-5
a19=1, b19=11, c19=-6
a20=1, b20=12, c20=-7
a21=2, b21=-7, c21=11
a22=2, b22=-6, c22=10
a23=2, b23=-5, c23=9
a24=2, b24=-4, c24=8
a25=2, b25=-3, c25=7
a26=2, b26=-2, c26=6
a27=2, b27=-1, c27=5
a28=2, b28=0, c28=4
a29=2, b29=1, c29=3
a30=2, b30=2, c30=2
a31=2, b31=3, c31=1
a32=2, b32=4, c32=0
a33=2, b33=5, c33=-1
a34=2, b34=6, c34=-2
a35=2, b35=7, c35=-3
a36=2, b36=8, c36=-4
a37=2, b37=9, c37=-5
a38=2, b38=10, c38=-6
a39=2, b39=11, c39=-7
a40=3, b40=-7, c40=10
a41=3, b41=-6, c41=9
a42=3, b42=-5, c42=8
a43=3, b43=-4, c43=7
a44=3, b44=-3, c44=6
a45=3, b45=-2, c45=5
a46=3, b46=-1, c46=4
a47=3, b47=0, c47=3
a48=3, b48=1, c48=2
a49=3, b49=2, c49=1
a50=3, b50=3, c50=0
a51=3, b51=4, c51=-1
a52=3, b52=5, c52=-2
a53=3, b53=6, c53=-3
a54=3, b54=7, c54=-4
a55=3, b55=8, c55=-5
a56=3, b56=9, c56=-6
a57=3, b57=10, c57=-7
a58=4, b58=-7, c58=9
a59=4, b59=-6, c59=8
a60=4, b60=-5, c60=7
a61=4, b61=-4, c61=6
a62=4, b62=-3, c62=5
a63=4, b63=-2, c63=4
a64=4, b64=-1, c64=3
a65=4, b65=0, c65=2
a66=4, b66=1, c66=1
a67=4, b67=2, c67=0
a68=4, b68=3, c68=-1
a69=4, b69=4, c69=-2
a70=4, b70=5, c70=-3
a71=4, b71=6, c71=-4
a72=4, b72=7, c72=-5
a73=4, b73=8, c73=-6
a74=4, b74=9, c74=-7
a75=5, b75=-7, c75=8
a76=5, b76=-6, c76=7
a77=5, b77=-5, c77=6
a78=5, b78=-4, c78=5
a79=5, b79=-3, c79=4
a80=5, b80=-2, c80=3
a81=5, b81=-1, c81=2
a82=5, b82=0, c82=1
a83=5, b83=1, c83=0
a84=5, b84=2, c84=-1
a85=5, b85=3, c85=-2
a86=5, b86=4, c86=-3
a87=5, b87=5, c87=-4
a88=5, b88=6, c88=-5
a89=5, b89=7, c89=-6
a90=5, b90=8, c90=-7
a91=6, b91=-7, c91=7
a92=6, b92=-6, c92=6
a93=6, b93=-5, c93=5
a94=6, b94=-4, c94=4
a95=6, b95=-3, c95=3
a96=6, b96=-2, c96=2
a97=6, b97=-1, c97=1
a98=6, b98=0, c98=0
a99=6, b99=1, c99=-1
a100=6, b100=2, c100=-2
a101=6, b101=3, c101=-3
a102=6, b102=4, c102=-4
a103=6, b103=5, c103=-5
a104=6, b104=6, c104=-6
a105=6, b105=7, c105=-7
a106=7, b106=-7, c106=6
a107=7, b107=-6, c107=5
a108=7, b108=-5, c108=4
a109=7, b109=-4, c109=3
a110=7, b110=-3, c110=2
a111=7, b111=-2, c111=1
a112=7, b112=-1, c112=0
a113=7, b113=0, c113=-1
a114=7, b114=1, c114=-2
a115=7, b115=2, c115=-3
a116=7, b116=3, c116=-4
a117=7, b117=4, c117=-5
a118=7, b118=5, c118=-6
a119=7, b119=6, c119=-7
a120=8, b120=-7, c120=5
a121=8, b121=-6, c121=4
a122=8, b122=-5, c122=3
a123=8, b123=-4, c123=2
a124=8, b124=-3, c124=1
a125=8, b125=-2, c125=0
a126=8, b126=-1, c126=-1
a127=8, b127=0, c127=-2
a128=8, b128=1, c128=-3
a129=8, b129=2, c129=-4
a130=8, b130=3, c130=-5
a131=8, b131=4, c131=-6
a132=8, b132=5, c132=-7
a133=9, b133=-7, c133=4
a134=9, b134=-6, c134=3
a135=9, b135=-5, c135=2
a136=9, b136=-4, c136=1
a137=9, b137=-3, c137=0
a138=9, b138=-2, c138=-1
a139=9, b139=-1, c139=-2
a140=9, b140=0, c140=-3
a141=9, b141=1, c141=-4
a142=9, b142=2, c142=-5
a143=9, b143=3, c143=-6
a144=9, b144=4, c144=-7
a145=10, b145=-7, c145=3
a146=10, b146=-6, c146=2
a147=10, b147=-5, c147=1
a148=10, b148=-4, c148=0
a149=10, b149=-3, c149=-1
a150=10, b150=-2, c150=-2
a151=10, b151=-1, c151=-3
a152=10, b152=0, c152=-4
a153=10, b153=1, c153=-5
a154=10, b154=2, c154=-6
a155=10, b155=3, c155=-7
a156=11, b156=-7, c156=2
a157=11, b157=-6, c157=1
a158=11, b158=-5, c158=0
a159=11, b159=-4, c159=-1
a160=11, b160=-3, c160=-2
a161=11, b161=-2, c161=-3
a162=11, b162=-1, c162=-4
a163=11, b163=0, c163=-5
a164=11, b164=1, c164=-6
a165=11, b165=2, c165=-7
a166=12, b166=-7, c166=1
a167=12, b167=-6, c167=0
a168=12, b168=-5, c168=-1
a169=12, b169=-4, c169=-2
a170=12, b170=-3, c170=-3
a171=12, b171=-2, c171=-4
a172=12, b172=-1, c172=-5
a173=12, b173=0, c173=-6
a174=12, b174=1, c174=-7
a175=13, b175=-7, c175=0
a176=13, b176=-6, c176=-1
a177=13, b177=-5, c177=-2
a178=13, b178=-4, c178=-3
a179=13, b179=-3, c179=-4
a180=13, b180=-2, c180=-5
a181=13, b181=-1, c181=-6
a182=13, b182=0, c182=-7
a183=14, b183=-7, c183=-1
a184=14, b184=-6, c184=-2
a185=14, b185=-5, c185=-3
a186=14, b186=-4, c186=-4
a187=14, b187=-3, c187=-5
a188=14, b188=-2, c188=-6
a189=14, b189=-1, c189=-7
a190=15, b190=-7, c190=-2
a191=15, b191=-6, c191=-3
a192=15, b192=-5, c192=-4
a193=15, b193=-4, c193=-5
a194=15, b194=-3, c194=-6
a195=15, b195=-2, c195=-7
a196=16, b196=-7, c196=-3
a197=16, b197=-6, c197=-4
a198=16, b198=-5, c198=-5
a199=16, b199=-4, c199=-6
a200=16, b200=-3, c200=-7
a201=17, b201=-7, c201=-4
a202=17, b202=-6, c202=-5
a203=17, b203=-5, c203=-6
a204=17, b204=-4, c204=-7
a205=18, b205=-7, c205=-5
a206=18, b206=-6, c206=-6
a207=18, b207=-5, c207=-7
a208=19, b208=-7, c208=-6
a209=19, b209=-6, c209=-7
a210=20, b210=-7, c210=-7

Write each equation on a new line or separate by a semicolon. Unknows are a,b,c ... z. A Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are studied. An integer solution is a solution such that all the unknowns take integer values). Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations.

Examples of Diofant equations and problems: